Your first instinct, when you see an extraordinary new building that looks like nothing you have ever seen before, is to try to understand it by connecting it to what you know. And so Frank Gehry’s new Fondation Louis Vuitton, in Paris, looks like sails, and it looks like a boat, and it looks like a whale, and it looks like a crystal palace that is in the middle of an explosion. Some of the innards make you think of Piranesi, and as you look up the stair tower, monuments of Russian Constructivism, such as Vladimir Tatlin’s fantastic spiral tower, might flash through your mind, just as you could stand in front and from one angle the façade could make you think of Frank Lloyd Wright’s Beth Sholom Synagogue, his great “Mount Sinai in glass.”

But none of these comparisons matter in the slightest. They’re all correct as far as they go, but they are really only ways of postponing coming to terms with the fact that this building is a whole new thing, a new work of monumental public architecture that is not precisely like anything that anyone, including Frank Gehry, has done before. You could call it a 21st-century take on the Grand Palais, the wildly extravagant Beaux-Arts exhibition hall off the Champs-Élysées, and you could also say that it’s Gehry’s attempt to render his own Guggenheim Bilbao in glass. But even these, which get closer, miss a lot of what makes this building remarkable, just as calling it a descendant of Gehry’s IAC office building, in New York, which is made up of billowing white glass that also always reminds people of sails, only begins to explain what Gehry has wrought on this unlikely site within the Bois de Boulogne at the western edge of Paris.

Gehry, who is now 85, continues to push himself forward, as Picasso and Wright did late in their careers, relentlessly determined that, however important his past work may be, it must serve for him as the foundation for something more than a mere dénouement. He has been experimenting with curving glass for years, twisting and torquing it into lyrical, dancing shapes, and here the long quest that began with the glass panels decorating the cafeteria he designed for the Condé Nast Building in 1999 culminates in enormous glass sails that are pieces of architecture in themselves, sumptuous forms that give shape to an entire building.

Gehry loves the form of the fish as much as he loves sailing and boats, and it is not hard to see this building as the moment when these preoccupations come together into one gargantuan and complex object. Yet another longtime theme in Gehry’s work has been his desire to tear away the façades of his buildings, making the structure—what he calls “the bones”—visible as a way of celebrating the aesthetic hidden within it, and what began decades ago when he started revealing the wooden framing inside the walls of small houses has grown here into exhibiting vast and monumental curves of steel and timber, a framework that seems at once to evoke the Eiffel Tower and an ancient church. This building is muscular, and it is delicate: it is a linebacker with the moves of a ballerina or, if you prefer, it is Moby-Dick with the athleticism of a sailfish.

The reported $143 million Fondation Louis Vuitton, which opens to the public in October, was commissioned by Bernard Arnault, the chairman and C.E.O. of the luxury-goods conglomerate LVMH Moët Hennessey Louis Vuitton, as a contemporary-art museum and cultural center, and it is not only its architecture that is unusual. There are relatively few private museums in France, and in building this one Arnault—himself a major collector—was obviously hoping to reinforce a connection between his company and advanced art and design. But it has the potential to develop a brand even more potent than that of LVMH: that of France itself, and of Paris, where more creative energy surrounded modern art, architecture, and design in the first half of the 20th century than anywhere else. Paris long ago ceded its leadership as a creative center to New York and other cities, and not even the vast investment of the French government in such architecturally ambitious projects as the Centre Pompidou, by Richard Rogers and Renzo Piano, the expanded Louvre, with its glass pyramid, by I. M. Pei, and the Cité de la Musique, by Christian de Portzamparc, has been enough to get it back.

But not until now has there been a significant private investment in a cultural institution, a new entity conceived, designed, constructed, and managed without the heavy hand of French bureaucracy. Gehry’s building—which is his first project in Paris since he completed the American Center, now the Cinémathèque Française, in 1994—is the most compelling work of new architecture the city has seen since the Centre Pompidou opened, almost 40 years ago, and the new museum and cultural center it houses represent the unbridled zeal of the private sector. Paris has never experienced a marriage of cultural ambition and private enterprise of this magnitude, and it may have a shot at making something happen that extends way beyond Gehry’s glass doors.

Its roots go back to 2001, when Jean-Paul Claverie, who joined LVMH as a special adviser to Arnault after working under Jack Lang in the French Ministry of Culture, became so excited about Gehry’s Guggenheim Museum, in Bilbao, that he insisted that Arnault make a trip to Spain to see it. “I wanted him to discover it and share with me the feeling I had standing in front of it,” Claverie said to me. “It wasn’t easy—he canceled twice, but finally we succeeded in November of 2001,” when Arnault, face-to-face with Gehry’s building, Claverie recalls, could say only, “How can a person imagine this architecture?”

Arnault said he had to meet Gehry, who is based in Los Angeles, and the two arranged to have lunch a month later in New York. Arnault told Gehry that he envisioned a building in Paris that would embody his Louis Vuitton Foundation for Creation’s mission to support the arts and education and that he wanted it to be a significant work of architecture.

“The building was to be the first artistic act of the foundation,” Claverie, who was put in charge of the project, said to me. He and Arnault took Gehry to the site, which is at the Jardin d’Acclimatation, a children’s park toward the northern end of the Bois de Boulogne. The location might seem to make little sense: the cultural energy of Paris has been shifting to the east for years.

Arnault had his reasons, however. Although the Jardin d’Acclimatation was inside a public park, its concessions were owned by LVMH. And since Arnault had always wanted a striking piece of architecture—“a haute couture building,” in Claverie’s words—he hoped that erecting it in the Bois de Boulogne (construction began in 2008) would free him and Gehry from the inevitable battles that ensue whenever anyone tries to insert a strong piece of modernist architecture into the Parisian streetscape. They hardly had carte blanche, however. The city government first insisted that the building not be taller than the low, boxy one that had previously occupied the site, and later, after Gehry’s final design was approved, there were objections from a NIMBY group that protested with the zeal of people for whom the notion of backyard meant the entire Bois de Boulogne. (The nearest residents were actually a couple of blocks away.)

Gehry, for his part, had to relate his design mainly to trees and lawn, which for him was almost too easy. Gehry likes his buildings to play off their surroundings, not by mimicking them but by shifting shapes, focusing vistas, or raising their heads high at a particular moment, such as the way the tower of the Guggenheim in Bilbao acknowledges a nearby bridge and the industrial heritage of the adjacent river. The 126,000-square-foot Fondation Louis Vuitton is surrounded mainly by open space and trees, and Gehry’s sculptural instincts could run freer here than in many of his buildings.

Paradoxically, this probably made designing the building all the harder, because there was no clear starting point other than the foundation’s desire for lots of gallery space, an auditorium, and the usual public amenities such as a café, a bookstore, and a large central lobby. Gehry designed the building from the inside, starting not with the final shape but with three piles of boxes containing art galleries, and three circulation towers, containing stairs and elevators. “You can’t hang art on glass,” he said to me. It is the way Gehry usually works—for all he is identified with striking sculptural shapes, he almost never starts with them, because he wants to be sure that the functions of a building are taken care of before he starts letting his sculptural instincts run free. The gallery sections—which will house a corporate collection featuring works by Jeff Koons, Richard Prince, and others—are covered in a white fiber-reinforced concrete called Ductal, which led Gehry to name them “the icebergs.” He then began to arrange an array of curving glass pieces over the icebergs and towers, precisely composed to serve as both façade and roof, as well as to enclose the lobby and to cover the roof terraces. “I could do neutral galleries, and I could do me at the same time,” Gehry said.

Here, too, Gehry is referencing his earlier work, since one of the things he did a lot of before he started creating unusual, curving shapes was to make buildings that consisted of unevenly stacked boxes. In Paris, he has taken that old idea and re-invigorated it by connecting it to his most assertive structural leap, the huge glass sails. It is a hint of early Gehry wrapped in late Gehry, but without a whiff of nostalgia—this is less a case of looking back than of reaching back and grabbing a piece of the past and pulling it along into the future. (The building also features an auditorium facing a waterfall that tumbles down a series of steps and helps bring natural light down into the space, which will be used for LVMH fashion shows.)

Gehry has often been accused, mostly unfairly, of making architecture that overwhelms art, but it will be harder to level such charges at the Fondation Louis Vuitton, because the icebergs make for relatively neutral galleries—not plain white boxes, which Gehry is probably incapable of producing, but rooms that for the most part are shaped like rectangles with straight, flat walls. When there is no art in the building, it feels incomplete, which is arguably the most important test of whether the architecture is too assertive. “It makes me crazy when people say, ‘Oh, Frank, your architecture is too complicated—it’s overpowering the art,’ ” Gehry said to me. “I’ve talked to artists, and they’re willing to play.” In Paris, Gehry has come closer than ever before to having it both ways—to showing art in straightforward rooms that just happen to be part of an utterly spectacular building, one that only heightens the intensity of the art within.

More than 50 years ago, when his career was just beginning, Gehry spent a year in Paris working in an architect’s office, and he discovered European architecture for the first time. He was struck by everything he saw, but most of all by the powerful, heavy forms of Romanesque churches and the lyrical lines of late buildings of Le Corbusier, particularly his great chapel at Ronchamp. You can see all of this in the Fondation Louis Vuitton: the strong structure, the soft curves, the whole idea that a building is a sensuous experience. Gehry has been exploring these ideas for a long time, but they have a particular resonance here, as if he knows how deep his debt to French architecture is, and he saw this building, most of all, as a chance to pay it back.