Why Gustave Courbet still has the power to shock

"When I stop being controversial, I'll stop being important," Gustave Courbet wrote to his parents in 1852. He was in his early thirties, and starting to be controversial. His monumental frieze of provincial life, A Burial at Ornans, had taken a critical beating - as ugly, brutal, vulgar, mindless - when shown in Paris the year before. But he speaks with the voice of a seasoned avant-gardist, a voice that was more and more often heard in the ensuing century. He's not waiting for the fuss to die down, pinning his hopes on calm posterity and proper recognition. Like the Dadaists in the 1920s, or the Situationists in the 1960s, so for Courbet in his prime, the fuss, the fight, the struggle now, is what it's all about.

And long after he was in all the museums, Courbet stood as a symbol of struggles to come. The uncouth paintings he made in the middle of the 19th century, The Stone Breakers, A Burial, The Meeting, The Bathers, stayed important because they pointed ahead. For some they heralded modern art. Their physicality, flat-on compositions and claggy paint-surfaces led to Cezanne, and Cubism. For others they prophesied the revolution. Courbet called himself a socialist painter, was friends with Pierre-Joseph "property is theft" Proudhon, and was imprisoned for his part in the Paris Commune. He showed what an art of the people might look like.

Those struggles no longer continue. Modern art triumphed, and passed. The revolution failed. But Courbet continues, and continues to affront. The exhibition of his work that's just opened at the Grand Palais in Paris stresses the breadth of his achievement, the way it extends far beyond the solid, epic images of low-class life with which he made his stamp. There are masterpieces in every genre - portraiture, landscape, seascape, nudes, animals, still life - a legacy of unforgettable images.

Impressive, yes. But with Courbet, "achievement" seems the wrong word. His art doesn't settle into the wisdom of the ages, or find its place in the pantheon. Much of it still remains crude, dour, obdurate, indigestible, sometimes aggressively blunt, sometimes defensively withdrawn. Its affront isn't the usual radical gesture of shock and transgression, which can always be enjoyed. Courbet is powerful, but not entirely enjoyable. What was his beef?

Self-importance perhaps; unassuagable egomania. Born in 1819, in Ornans in the Franche-Compte, he insisted that he was a self-made painter, with no art training. Not quite true, but he was largely self-instructed, drawing on Rembrandt and the solemn naturalism of 17th-century Spanish painting, as well as on his immediate Romantic predecessors. His early self-portraits declare an extreme self-regard.

The artist appears before us as a lover, as a blood-stained corpse, as a man staring madly at himself in a mirror and - most bizarrely - as a man in mid-suicide, caught in the act of jumping off a cliff. Sometimes the eyes are closed or in shadow. Even when they seem to look at us, they're really looking straight through us. In one form or another, a defiant disregard of his audience is Courbet's secret.

"Realism" was his slogan. The newly coined term was already rich in meanings. It meant sticking to the real world ("I cannot paint an angel, for I have never seen one"). It meant not beautifying. It meant low-class, provincial subjects. It meant a dense, thingy, way of painting. But in Courbet's hands it involved both an affirmation and a negation. The subject is presented with unbudgeable material sturdiness. But there's a refusal to make the scene fully available to the viewer.

In After Dinner at Ornans, there is the man who sits, centre front, with his back to us. That's an obvious sign of our exclusion. In The Peasants of Flagey Returning from the Fair, it's the man with the umbrella and the pig on a lead, walking straight across the front of the picture, who disrupts our ability to take in the steady, solemn procession of men and cattle. In two key scenes of labour, both missing from the exhibition - The Stone Breakers and The Winnowers - the protagonists are turned away, their faces hidden, their gestures abrupt. Our emotional involvement is held off. Meanwhile, in A Burial we're confronted with a huge, dense wall of life-size figures, which the picture utterly declines to arrange into any comprehensible hierarchy or story or relationships.

It is depiction as obstruction, putting the world unignorably in our way, giving it a grand and massive presence, while at the same time allowing the spectator the minimum purchase on it. It was one reason that Courbet gave offence. Another was his staggering pretentiousness, his self-presentation as a heroic artist. In The Meeting, he appears, in the middle of open country, as a staff-bearing wanderer being greeted by his patron and his servant: it might be Christ appearing to two disciples. In The Painter's Studio - subtitled A Real Allegory, Which Determined a Seven-Year Phase in my Artistic and Moral Life - he treats himself to a panoramic multi-figure apotheosis, himself at the easel, flanked by various significant contemporaries.

Courbet against the world - or, as Baudelaire sarcastically put it, "Courbet saving the world". But what exactly his mission was has never been easy to determine. He styled himself "Gustave Courbet, master-painter, without ideal and without religion". In Paris, he played up his hearty, beery, rustic masculinity. He assumed any number of oppositional roles, postures of resistance: provincial peasant; bohemian outsider; socialist revolutionary; medieval artisan; pilgrim; atheist materialist. His signature is almost a logo, the letters spelled out in a hand-painted typeface, like a maker's stamp.

That figures. The disconcerting thing about Courbet's self-importance is that there seems to be nothing personal in it. It's not about him. In The Painter's Studio, though the central figure, he is again half turned away, getting on with his painting. It's just that he has this very important job to do. Or so he felt, at least, up to a certain stage in his career. The turning point is probably the one-man "Pavilion of Realism" he set up in Paris in 1855, the year of the Universal Exhibition - a bid for completely independent artistic status, an attempt to establish himself as a public entity in his own right. Critically and financially, the project bombed.

The Grand Palais arranges the work mainly by genre, all the craggy landscapes together, all the nudes together, and this obscures chronology, and the way that Courbet's painting ceases, from the mid-1850s, to address the public world. The half-naked woman in The Bathers, her fat back turned (of course) as she strides away from us, is a public statement about class and female beauty. The later nudes are admirably pornographic, with no dissimulating about what they want and like, but they're for private consumption.

The hunting scenes are the most surprising. Courbet was a keen huntsman. The subject gives him an opportunity for an explicit emotionalism that is otherwise absent - in the melancholy solitude of the horseman at dusk, in the frightening combat of stags in the dark heart of the forest, in the tragic magnificence of the animal's death. But occasionally something more powerful appears: Poachers in the Snow has the blunt matter-of-factness of the "realist" pictures, two men and two dogs in laconic, faceless silhouette, moving fast.

Courbet's strength is in his impermeability. For all the palpable paint, the tough use of the palette knife, there's no manual virtuosity to be relished. Nor is he a clever painter. There are no witty juxtapositions, no surprising shapes, no neat arrangements, nothing that implies a performance. Even when he breaks the rules, introducing flagrant spatial or anatomical "errors", he does it with stubborn conviction, not with insolence. Manet is insolent. Courbet would never be so ingratiating - insolence implies a consciousness of your audience.

"Painting is an essentially concrete art and can only consist of the representation of real and existing things," said Courbet. And that seems to imply for him nothing more than real and existing things. Courbet's extraordinary close-up image of a woman's genitals, The Origin of the World, may have a fancy allegorical title, but what's extraordinary about it is not only its explicitness but its impassivity. Wholly physical, it dispels all erotic mystery or sentiment. Simply this.

Or there's that late painting The Trout, done while he was in prison. A hook in its open mouth, it's laid out on a bank, head up, so with some signs of life, and close framed, as for its portrait. You can hunt for pathos in it - surely a displaced self-portrait? - or for the utter desolation that Goya puts into dead meat. They're not really there. Again, simply this.

It is Courbet's great refusal. In his best work he paints facts without meanings. He makes things heavily present, but beyond an emphatic material existence, every moral or "ideal" that might be aroused, every kind of appeal to the viewer, is refused. It is the most deadpan, stony-faced, ungiving art. It resists us still.

Gustave Courbet, Grand Palais, Paris (00 331 4413 1717), to 28 January