Marion Cotillard: I haven't lost my legs, but I have lost and I have felt pain

There's a theory that the best way to win a best actress Oscar is by a dramatic change in appearance. From young to old, beautiful to haggard, from Meryl Streep to Margaret Thatcher. At least no-one can accuse Marion Cotillard of deliberate Oscar-hunting. She already has one, for playing French chanteuse Edith Piaf in 2007's La Vie en Rose. Nevertheless in her new film Rust and Bone, which won Best Film at the London Film Festival last weekend, Cotillard transforms strikingly to play a double amputee called Stéphanie. Her hair hangs lank, her eyes are half-dead. And you can't take your eyes off her.

Today, the actress is dressed in Dior – she's a "face" for the fashion house – and looks like Paris in the springtime. She, apparently, finds her beauty irrelevant, being more interested in losing herself in a part. When her Rust and Bone co-star, the Belgian actor Matthias Schoenaerts, first met her on the set, Cotillard was in her wheelchair, sullen and silent. She was already Stéphanie, a sea-world trainer who loses her legs in a freak accident. Ali, a rough bouncer, played by Schoenaerts, is the only one who doesn't treat her like an invalid. As a love story, it's a bruiser. Made by Jacques Audiard, director of A Prophet, it's been a critical hit at festivals including Cannes, Toronto and London.

Despite the difficulties of transforming for her previous role as Piaf, Cotillard describes this film as "her biggest challenge so far".

"I wanted to work with Jacques Audiard. Even before we met, he was on my to-die-for director list. And then there is Stéphanie. Usually, I connect emotionally with a character, and I discover all the layers. But with her, I freaked out. There is something so mysterious about her, I felt I didn't know her at all."

You could almost level the same accusation at the actress. She speaks perfect English, pausing frequently to find the right word and answers honestly. Yet she doesn't give herself away easily. Her parents and her younger twin brothers are all in the business. Acting was the only option.

Now 37 she has been with her partner, the director Guillaume Canet, since 2007. They originally met 10 years ago, on the set of Love Me If You Dare. Their son Marcel was born 18 months ago. Although she and Canet have the tag of "France's Brangelina", they live quietly, solidly, together in Paris. They last collaborated together on Little White Lies in 2010, a tale about dysfunctional thirtysomethings which was a hit in France. She smiles wryly at the memory. "In some ways it is great to be directed by your partner, because then you can always be together. But we did talk constantly about work and it came off set with us. However, I guess he did something right because I have promised him I will work with him again."

Rust and Bone was one of the first films she signed up for after the birth of Marcel. Seeing the actress without legs is a punch in the guts – even if it is just CGI. She says she didn't do any research into amputees, apart from watching footage of how to move. "It was not so much the physicality of the part that interested me, but the emotion. I haven't lost my legs, but I have lost, and I have felt pain. I knew the CGI would work, because otherwise, there was going to be no movie.

"The first scene I did without legs, I was in a wheelchair, so my legs were bandaged up underneath me. In every scene, the CGI people were so quick, and so discreet, that I barely noticed them. I have to say, when I saw it for the first time in a cinema, I was amazed. It is so powerful."

By "discreet", she is referring to the numerous sex scenes she and Schoenaerts had to perform. An image of her naked, amputated body appears in the film trailer, something Cotillard approves of: "The sex and flesh is part of the story," she says. " It's not sensational or a statement at all, it had to be in there. You know how you feel when you rediscover your body, love, your life. That's what happens to both these characters and I think that is very sexy."

Ever since she was discovered, aged 21, with a part in Arnaud Desplechin's comedy My Sex Life... or How I Got into an Argument, the parts Cotillard has chosen have been far from feeble French flowers; from Tina Lombardi in Jean-Pierre Jeunet's A Very Long Engagement, who gets guillotined for murder; to bisexual headcase Marie in Little White Lies. She even smacked Russell Crowe in the face in A Good Year.

The Hollywood parts she has been offered post-Oscar seem feebler: a moll in Public Enemies with Johnny Depp; a cheated-on wife in the Rob Marshall musical Nine and love interest Miranda in The Dark Knight Rises. Christopher Nolan put off filming the latter because he wanted her in it, and at the time of asking the actress was pregnant with Marcel. "He called me up after Inception", she recalls, "And it was something I really wanted to be part of, but of course I couldn't. So he said, 'I am writing at the moment, let me see what I can do for you.' I feel so lucky that he would do that for me – the guy is a creative genius. I mean, it was amazing to be part of one of the biggest films ever made, but I don't feel with Christopher that I am making a blockbuster. He is a completely independent thinker."

As the first actress since Sophia Loren in 1973 to win an Oscar for acting in a foreign language, Cotillard isn't ungrateful to Hollywood. "I am so lucky to be able to work in both France and America. Most of the movies that fed my dreams as a child were American. The Oscar opened a door, there is no doubt about that. And perhaps there will be more doors opened because of The Artist's success too. French cinema is travelling, and I am proud to be a French actress. We are an old country of cinema."

You get the feeling that Cotillard will only ever keep dipping her toe into the studio system. She claims to like the "difficult" roles "in whatever language I can get them. Often, they aren't found in English. I want to explore and learn all my life", she explains. "Even when I am old. Before I am an actress, or a mother, I am a woman first. I feel that very deeply in my heart."

'Rust and Bone' is released on 2 November

This article will appear in the 27 October print edition of The Independent's Radar magazine