Paris is the city that invented the modern-day icon project, indeed is composed almost entirely of them. Its landscape has been reworked by successive rulers — Louis XIV, Napoleon, President Mitterrand — as their epitaph, stamping the capital with grands projets in their image (l’état, et l’architecture, c’est moi), while burying political sins with good old-fashioned bread and circuses.

Yesterday President Chirac opened his own projet, the Musée du Quai Branly, in the shadow of the Eiffel Tower beside the Seine, the biggest new museum to open in Paris since President Pompidou’s in 1977. Beaubourg exorcised the spirit of ’68. Can Quai Branly, Chirac’s valedictory gift as he shuffles off the world stage, be his epitaph and the saviour of modern, sullen, Paris?

As an epitaph to a presidency, Chirac really couldn’t have chosen a more controversial subject. The new museum contains that stunning national collection of ethnographic artefacts that so entranced Modernist artists in Paris — it is Chirac’s passion, too, as the self-styled “great defender” of global culture. But at a time of national soul-searching over the stagnant economy, the loss of the Olympics and the recent race riots, this is bold indeed. True to form, the project has been dogged with controversy — not just the usual “will it be finished in time” (not quite), the cost (£180 million), the “Elgin Marbles” debate, but its very purpose.

Quai Branly sidesteps the “Elgin Marbles” debate by presenting the museum as a museum of the world, “dedicated to the dialogue between cultures and civilisations”, said Chirac at its inception in 1994, designed to “accord tribal arts their true place in the story of mankind”. This implies that the collections are in Paris purely by serendipity, rather than by the efforts of some of the most voracious colonial collectors in European history. It is an attempt to rewrite history in concrete, so that Chirac’s presidency won’t be remembered for race riots but for making over the nation, and Paris, as the cultural crossroads of European multiculturalism — not London, the old enemy, with all its fusion food and chicken tikka masala.

The tricky bit is rendering multiculturalism in built form. Architecture doesn’t lend itself easily to fusion. By its very nature it tends towards the absolute. You wouldn’t catch Napoleon and Mitterrand going for wussy “dialogue”. It is possible, though, with an architect of rare skill, to create the subtle architecture required, while delivering that vital iconic panache.

If anyone can do this, Jean Nouvel can. France’s lone architectural superstar is less interested in steel and glass to create wham-bam statements than in using their visual and physical qualities to form architectural experiences of doubt and intrigue. His buildings, inspired by Islamic architecture and French postmodern philosophy, uncurl themselves around you in dizzying trompe l’oeil spaces, like walking through a labyrinth of smoke and mirrors. They deliver the iconic punch, too. Of all Mitterrand’s projets it’s Nouvel’s Institut du Monde Arabe (1987) and Fondation Cartier (1994) that still shine.

Nouvel’s manifesto for Quai Branly is, on paper, perfect. “Material form seems to melt away,” he says. This is less a building than a “sacred wood” in which to “discover” the objects “liberated from Western architectural references such as barriers, showcases, railings”. The conceit of discovering objects in a dark forest is, perhaps, contentiously Eurocentric. But as architectural form it could thrill. It did ten years ago in his Fondation Cartier. What the hell happened here, though?

True, there are characteristically magnificent theatrical flourishes: the giant, Seine-side wall of vegetation; the city-side wall where bold works by aboriginal artists bleed from the building’s ceilings into the street through mirrored window soffits; the languidly double-curling entrance r the huge, terraced “forest” garden.

Magnificent fragments, though, which fail to glue together. The lack of an external “iconic” image is intentional: the chunky building tries (but fails) to hunker down into the cityscape. Inside, though, you expect more elegance from Nouvel. Perhaps it’s the departure from his expertise — ambiguity through glass — to new, fashionable architectural territory — ambiguity through playing with the solid object — that grates.

In the main galleries, spotlit objects in a crepuscular forest are laid for discovery along a serpentine ravine of promenades and terraces. But there are neither the thrilling jump-cuts of a Libeskind or Koolhaas, nor elegant flows between them, like a Hadid. It jolts, cumbersome and heavy. This is a building that never quite resolves itself: not fusion food, but a stew of rich, mismatched ingredients. A saviour for the city? No chance. But, eccentric, incoherent and full of unresolved doubts, it’s the perfect epitaph for Chirac.

Musée du Quai Branly (www.quaibranly.fr) opens on Friday. Closed Mondays