Wandering through the rue des Martyrs in 1908, Picasso stopped beside an upholstery shop. "A head peered out, the face of a woman, hard eyes, a penetrating look, decisiveness and clarity. The canvas was huge. I enquired about the price. 'A hundred sous,' replied the dealer. 'You can paint over it.' It was one of the truest portraits ever of the French psyche."
Henri Rousseau's five-franc, life-size woman in Van Dyck black, unsmiling and erect before a chintz curtain as if she were posing for a local photographer, stayed at Picasso's side until his death, longer than any flesh-and-blood muse. A century later, she towers over us at Tate Modern's Rousseau retrospective as imperiously as a Velázquez monarch. You can see why Picasso fell for her even though the naive style in 1908 made self-taught Rousseau a laughing stock.
But ever since, the douanier has been one step ahead of the avant garde. He was the customs officer who crossed the border to modernity without realising he had done so. For the early modernists, he was a Gauguin of the suburbs, embodying the primitivism they sought in non-European art. To Fernand Léger he was "our father", to Max Beckman "Homer of the porter's lodge", and in his hyper-realism the surrealists in turn found a hero. Through a democratising 20th century, Rousseau was popular, accessible, a class warrior - the low-grade civil servant turned world-class artist without selling out to bohemia. His downtrodden life, petit bourgeois pieties, inept bons mots - "You know, I could finish all these canvases," he offered at Cézanne's posthumous exhibition in 1907, impervious to the self-doubting agony that had prevented the master doing so himself - all are lovable legends.
In this 21st-century retro-spective Rousseau is our contemporary still: a conceptual artist whose painterly awkwardness ceases to matter, a fantasist for a fantasy-dependent age.
The spacious, gracious installation of large-scale paintings at Tate Modern looks spectacular. Though familiar, the lithe animal snarling through giant ornamental houseplants in the National Gallery's "Tiger in a Tropical Storm (Surprised!)" makes a magical opening, the lightning flashes and fragile, transparent grey-white glazes of streaked rain creating an all-over striped patterning that gives weight and unity. Rousseau painted it in 1891, then abandoned jungle themes until 1904, when he modelled "The Hungry Lion Throws itself on an Antelope" on beasts from the Natural History Museum. In a fascinating display, Tate shows these stuffed creatures surrounded by films and memorabilia from the Jardin des Plantes and Paris's World Exhibitions, Rousseau's inspiration - he never left Paris, which is why his forests resemble theatre sets. These are the backcloth for a superb unfolding of the jungle works, borrowed from big museums, which are Tate's highlight.
Room after room reveal Rousseau's freshness, his audacious colouring, the precise detail of his mindscapes. "The Flamingoes" is a masterpiece of cool French harmony, a laconic Eden of olive palms jutted against turquoise water and lotus-plants on arabesque stems, evocative less of the jungle than of art nouveau motifs from the Paris metro. In a bizarre confrontation, "Fight between a Tiger and a Buffalo", enveloping textures of green - dark ferns, feather-thin grass blades, fleshy rubber plants - contrast with opulent oranges and bunches of bananas hanging like lanterns: one thinks of Hockney, Max Ernst, Gauguin and the hard-edged brightness of the Italian primitives, all at once.
There is the same monumental presence in the brooding "Snake Charmer"; the richly luminous "Jungle with Setting Sun", where man and tiger fight it out beneath a flat, bright disc in a vast sky; the statuesque nude in "The Dream" reclining "Olympia"-like on a red velvet sofa surrounded by jungle dreams of fauves and birds of paradise.
"When I am in the greenhouses and see the strange plants from exotic countries, it is as though I am experiencing a dream. I feel myself to be a completely different person," Rousseau confided. This is a vital clue. Follow this theatrical show from his first exhibited work, a moonlit mis-en-scène of a black Pierrot against a filigree pattern of icy branches in "A Carnival Evening" (1885), which amid general mockery drew admiration from Pissarro ("an atmospheric disposition as clear as glass, so complete in itself that one cannot think of it as the lucky accident of a beginner"), through jungle fantasies, cityscapes and portraits, andthe Jekyll and Hyde nature of Rousseau's temperament is in-escapable.
How could this dreamer of primeval life also have painted two-dimensional scenes of petit bourgeois routine, with hedgerows neatly trimmed and provincials in their Sunday best? Not competent to finish the feet of the uniformed troops in "The Artillerymen", he mires them instead in grass. Pompous dignitaries in "The Representatives of Foreign Powers Coming to Greet the Republic as a Sign of Peace", owned and lovingly laughed over by Picasso, are motionless tin soldiers, each comically clutching a laurel twig.
Rousseau was fabulously un-even. He never learnt basic rules of perspective or how to ground a figure in landscape, and it was this freedom from conventional rules, which the avant garde were seeking to unlearn, that endeared him to Picasso and especially those modernists experimenting with abstraction. Abstracted coils of fat treetrunks and schematised black fences and chimneys in "Landscape on the Banks of the Bièvre at Bic-être" echo in Léger's "tubism". The lovely glassy blue, porcelain green "View of Malakoff" was coveted by Kandinsky, a Rousseau collector, and influenced the formal rhythms of some of his quasi-abstract landscapes.
Rousseau's own tastes were conservative. Long after he had become the avant garde's holy fool, feted at a Picasso banquet where he snored his way through mockery and awoke with tears of gratitude after candle wax had dripped to form a dunce's cap on his bald head, he continued to admire regressive salon painters - Bouguereau, Cabanel. But his stubborn, clumsy style could not conform to academicism, flaring out instead in moments of dazzling originality or gaucheness.
Sometimes the two combined - as in the sturdy, defiant infant of "To Celebrate the Baby", its limbs disproportionate, its feet again concealed in grass. The child is as much an automaton as the puppet it dangles on a string, yet Rousseau catches precisely a baby's conviction of its own central importance. Observers noted similar qualities in Rousseau himself, along with a child-like capacity to lose himself in terrifying studio fantasies.
This, surely, is the root of his genius, of the timeless appeal of his jungles. But for me the most mesmerising painting here is the one large-scale work with no shade of green at all: the apocalyptic allegory "War" (1894). A wild girl gallops on a jet-black steed over a stony landscape of ashen trees, sooty clouds andalabaster corpses. The relentless child-angel of the apocalypse recalls Uccello's and Brueghel's death-riders on horseback, though Rousseau is unlikely to have known them, while looking ahead to the savage primitivism of Picasso's "Guernica" and "The Charnel House".
What other 19th-century work, besides Goya's, so presciently depicts 20th-century horror? Rousseau's great freedom was to imagine landscapes of fear and desire. They make him our contemporary in an individualist age when, as Picasso foresaw, "artists no longer live within a tradition, and each of us has to create his own possible modes of expression. Every modern artist possesses the right to create his own vocabulary from A to Z."
'Henri Rousseau, Jungles in Paris', Tate Modern, London SE1, tel 020 887 8888, November 3 to February 5, sponsored by Aviva. Grand Palais, Paris, March 13 to June 19, National Gallery of Art, Washington, July 16 to October 15
