Charlotte Gainsbourg: 'My parents put me second. But I like to think of them in Paris, having fun, not thinking too much'

If there is any great mystery about Charlotte Gainsbourg, then it is how she came to be so well adjusted.

The daughter of the French singer Serge Gainsbourg and the English actress Jane Birkin, Gainsbourg has been working since she was 12 years old, as an actress and as a singer. The talents of both her parents have found expression in Gainsbourg's own stellar career, as have their looks in her face and body. She has inherited their indestructible glamour too, their iconic status as people who expressed something important to the French of what it was to fully inhabit liberated, post-war Paris.

Because of their Russian-Jewish heritage, Serge and his family, under occupation, had first been forced to wear the yellow star and then to flee the capital, so the creative, social and sexual freedom he and his life came to represent was all the more precious to his country. This seems like an awful lot of expectation to have been saddled with. But there is nothing of the struggling adult victim of precocious child-stardom, or of self-absorbed celebrity parents, about this 38-year-old woman.

Gainsbourg is not beautiful in the way that her famous beauty of a mother was and is. In fact, she makes her mother's beauty seem almost contrived in its handsome conventionality, because in Gainsbourg's face one can see also the brooding, almost-ugly, physical magnetism of her father. Gainsbourg's beauty makes physical perfection look like the biggest yawn in the world. Her face is mobile, interesting, strong, uncompromising. Her body is graceful, expressive – especially her hands, which are much used as she talks intently in her measured, perfect English. At one point, as she speaks, Gainsbourg gathers her long, dark hair and twists it round her finger into a chignon. It's almost like a party trick, the way that all that hair disappears. There is not actually much of it, but what there is, she makes the most of.

Gainsbourg presents herself as a woman who cares little for fashion, or grooming. Rangy and lean in a classically generic casual outfit – jeans, a black sweatshirt and cowboy boots – Gainsbourg is not vain enough to make a big deal of her lack of vanity. A little diamond hangs from a short chain to nestle in her clavicle. On her eyelids, perfectly applied, a thin, dark swoop of liner adds a touch of softening artifice to that splendid, horsey face. Jewellery and make-up, just enough of it, signal that she does care about how she is seen and perceived, just enough.

Gainsbourg has a reputation as a prickly interviewee. But today anyway, she is disarmingly candid. She admits freely, for example, that when she was small, she mostly saw her parents as they returned from nights out, just as she and her half-sister – the photographer Kate Barry, Birkin's daughter by James Bond composer John Barry – were getting ready for school. Gainsbourg also marvels that at 13 or 14 she went off to shoot L'Effrontée, her second film, in Canada for two months, and had absolutely no contact with her parents the entire time she was working.

For a lot of people, these would be tragic vignettes, pitiful stories explaining why everything had unravelled in their lives. For Gainsbourg, though, they are happy memories, even though her attitude to her own children, Ben, 12, and Alice, six, and to her life with her husband, the film director Yvan Attal, with whom she is about to make a third film, is quite different to that of her own naughty parents.

"I'm sure I would have liked to have seen my parents more," she says, "and at that time, we did come second. But I like to think of them in Paris, having fun, not thinking too much ... And it was a different time. Now we're all trying to be more responsible, trying to do things the right way, and you get very, very guilty, really guilty. At the same time I think it must be awful to have a frustrated mother, turning down films. I never got that impression from my mother at all. She took us on shoots when she was able to, if it was holiday time she would take us wherever she was working.

"But I find it very difficult. The hours are just crazy in the sense that sometimes Yvan and I ... we're completely there, we have nothing to do, very lazy, because I have really big gaps and I like to have that time. And then suddenly the children don't see us, and we're rushing. With school becoming more and more important, it's so difficult to resist the impulse to just take them out of school, bringing them with me everywhere. But I have to accept that they have their own lives, things they have to do, friends ..."

Gainsbourg says that a couple of years ago, when her eldest was 10, she did wonder what on earth her parents had been thinking, to unleash her into the acting profession so young. "I thought: I can't imagine being a mother and letting go of your child to be on a set. Now I can understand. Two years ago, I thought: it's impossible. But I do see that there's something blooming, and I think about how lucky I was to be in that position. I have a tendency to not let go. But I can see the good of my children having a life of their own."

Gainsbourg's own careful reverence for her parents – she has been preserving her father's flat since he died when she was 19, in the hope that it will be made into a museum – and for her children, whose upbringing she frets over so much, make her involvement in Lars Von Trier's new film, Antichrist, seem all the more remarkable a choice. The controversial film is about a woman who is already being driven a little insane by the challenges of marriage and parenthood when her son falls from a window and dies as his mother and father make love. The psychological fall-out triggers terrible sexual violence and maiming, against her husband and against herself.

But Gainsbourg says there was not much in the way of a choice to be made. She was desperate to be in the film from the first time she read the script, even though she "didn't understand anything".

Gainsbourg is quick to qualify her initial claim to have been baffled by the script. "Well," she says, "that's not true, I understood some of it, but some of the clues, I didn't know what he [Von Trier] wanted to say, and what he meant. So I flew over to Denmark, met him. He didn't give me answers to my questions, and his questions I couldn't really answer either. He asked me if I had any panic attacks myself, or if I had in the past, really how anxious I was. He barely looked at me. I could see that he was in a bad state and I had a reaction to his anxiety, feeling very, very normal and secure with who I was.

"So, going back home, I thought, 'Oh, he'll never hire me'. But a few days later he said he wanted to do the film with me, but I had to agree that I was aware of what I had to do ... I could feel that he dreaded having an actress who would suddenly freak out and run away having said 'yes'.

"I hadn't met him before so I didn't know what kind of man he was, but he did explain in a very simple way that he had had a depression, that he was under heavy medication, and just trying to deal with his panic attacks that he had all the time. That was scary because he came up after the first week, to me and to Willem [Dafoe, her co-star], and explained that he didn't know if he could finish the film, that he didn't know how to cope with his attacks, that I would have to excuse him if he ran away, but he couldn't predict what would happen, and I was terrified at the thought that he would leave me – leave me on my own to make the film." She laughs.

Yet Gainsbourg must at least have understood something of the director's reputation. Von Trier is well-known to be weird and difficult, like his films, and is often accused of taking a misogynistic delight in placing immense pressure on his female leads. Those criticisms have become all the more virulent since Antichrist premiered at Cannes earlier this year. The film was greeted with critical outrage and contempt, although Gainsbourg herself waltzed off with a much-deserved award for best actress. Was she prepared for the reaction?

"When we knew we were going to Cannes, the publicist said I should prepare myself for heavy reaction, strong reaction, so ..." – she laughs – "I tried to prepare myself as best I could. And it was true that the press were virulent – they were quite shocked by the film. But, showing the film to the public the next day, the reaction was quite the opposite.

"So it was strange seeing the two reactions. Audiences applauded, they didn't laugh, they didn't boo. I was waiting for people to leave the theatre, scream ... but they didn't. They just ... stayed. So for me that was great. Then, coming back to Paris, some of my friends saw the film, some people I didn't know saw the film. And what they had to say was really interesting – compared with what the critics had been saying, because they were so cutting, saying that the film was misogynist and it wasn't a film to go and see."

Antichrist is certainly a film that is more interesting to talk about than actually to watch. Billed as a horror movie, it is completely without tension, with ponderous scenes displaying the unruly savagery of nature interspersed with therapist Dafoe's cruel and irresponsible attempts to "cure" his fragile wife of her grief and anxiety, and her own attempts to ease her psychological pain by losing herself in aggressive bouts of intercourse. "They have never been equal, those two," Gainsbourg declares with some passion. "He's always been paternalistic. For me, he always wanted to be the teacher, with her as his student. When she becomes the patient, he has got what he wanted."

Gainsbourg has a strong, basic grasp of what the film is attempting to express, the "duality between mother-woman and sexual-woman" but prefers not to "intellectualise" the film's most disturbing assertion, which is the female character's nascent belief that woman has an evil, primal, nature inside her, and a desire for annihilation. "I can't explain any of that. I do understand the closeness of women towards nature, once you deal with motherhood and all of that. At one point, for me, she goes into madness, and is possessed by what she calls demons.

"I had to imagine a relationship to the child, that wasn't written, that wasn't said, and I asked Lars how was I to be – was I to be a real mother? What did he want? And he said, 'No, there's no contact, you're just blank.' So he was already accusing the character of not being a mother, and I accepted that. For me it's part of a growing madness.

"I don't have the distance to analyse the film and to really understand it. People say, 'It's a misogynistic film: what do you think about his views on woman?' For me, I was playing him, in the sense that his vulnerability was what he was asking me to portray. And I had the impression that he was showing his fear of women and also putting women on a pedestal. And then, of course, he was breaking her down ..."

Gainsbourg appears to have relished the idea of delivering herself into Von Trier's hands. "He is demanding, that's for sure. But difficult – I don't think so. He wasn't difficult, I didn't feel a difficulty because I was willing to be manipulated, and I think I wanted that. I think I was quite masochistic at the time. I had been through a difficult year, I hadn't worked for a quite a bit, the Todd Haynes film [I'm Not There, the Bob Dylan biopic in which Gainsbourg played one of Dylan's wives, Claire] had come out, and I had had an accident also [a jet-ski accident, after which Gainsbourg had an emergency operation for a cerebral haemorrhage]. It was a hard time. I think I really needed to find something to put my head in and just work, so it was very helpful to get that film."

Despite Von Trier's manifest troubles, Gainsbourg says she considered him a father-figure and a man she wanted desperately to please. The parallels with her own father, who also dealt head-on with troubling sexual issues throughout his creative career – scandalising even the French when he featured his daughter in an album and a film hinting at incest – are, she agrees, part of the reason why she found it so easy to submit to Von Trier's demands. In his final years, after Jane Birkin had left him, Serge became notorious for drunken television appearances, in which he often mouthed obscenities. Some of Von Trier's recent work is so undisciplined and out-of-control that Gainsbourg's placid response to the sexual shock and chaotic ramblings can only be understood in terms of her abiding love for a father who latterly became, to some, "a national embarrassment".

Yet despite all his flaws and vulgar provocations, Serge's strengths – his musical originality, his lyrical genius, his ability to remain true to his own vision – are recognised and celebrated in Europe, now perhaps more than ever. Gainsbourg clearly sees something of her father in Von Trier. She sees the value in his work, even when it is hard for others to see it. Who is to say that she's wrong?

'Antichrist' opens nationwide on Friday