PARIS — The 18th-century bourse in the pulsing heart of this city has long been something of a landmark, its central location a boon to its former use as a wheat and corn exchange, its iron cupola so distinctive that Victor Hugo said it resembled an “English jockey cap.” Now the luxury goods billionaire François Pinault is racing to meet a self-imposed deadline to turn the building into a private museum by the end of 2018, spurred by the hope, he says, that art can offer solace to a nation scarred by terror attacks.

Last month, the Paris City Council approved the project, which calls for transforming the building into “The Pinault Collection, Bourse de Commerce” and filling it with art from Mr. Pinault’s collection of more than 3,000 works by contemporary artists like Andy Warhol, Damien Hirst, Gerhard Richter, Jeff Koons, Cindy Sherman, Agnes Martin and Cy Twombly. The interior is to get a makeover by the Japanese architect Tadao Ando.

“In the face of this barbarism, the only possible reaction is to move forward,” Mr. Pinault, 79, said in an interview, conducted in person and through email exchanges. “As André Malraux said, ‘Art is the shortest path from man to man.’ That is what prompted me to accelerate the completion of my project in Paris.”

The bourse looms over the newly revamped Les Halles shopping mall and transit point, where more than 750,000 people pass daily. It is one of a growing number of private museums around the world that match star architects and dramatic designs with ambitious billionaires — alliances that have sometimes brought questions about whether such pharaonic projects are a good use of public space, among other issues.

In this case, Mr. Pinault has struck a 50-year lease on the building with the City of Paris, and he is financing both the anticipated 50 million euro, or $55 million, makeover and future operating costs.

“My design is exactly the opposite of a pyramid,” said Mr. Pinault, a high-school dropout who built a lumber business into the luxury-goods conglomerate Kering, which includes the brands Gucci, Saint Laurent, Stella McCartney and Balenciaga. Now he is also a power in the art world, not only as a collector but also as the owner of Christie’s, the auction house.

His first attempt to build a museum in Paris, on an island in the Seine 11 years ago, was frustrated by bureaucratic hurdles and he abandoned his plans. Instead, he opened a contemporary art center in two historic palazzos in Venice, also renovated by Mr. Ando.

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For the new project, Mr. Pinault — who with his probing blue eyes appears younger than his years — is personally presiding over all its details with a small team of advisers, including a former French culture minister, Jean-Jacques Aillagon. On his smartphone, encased in a cover with a picture of his dog, Polka, he keeps photos of potential ideas for the museum, like a unisex bathroom that he spotted on a trip to Los Angeles.

“It is a project that must adapt and evolve constantly, and so it is not a monument frozen for all eternity,” Mr. Pinault said.

“This is not my mausoleum,” he added.

The plans are taking shape at the headquarters of Mr. Pinault’s investment group, Artemis, in a 19th-century mansion off the Avenue Montaigne that also mixes classic architecture with contemporary art.

Is there room in Paris for yet one more museum devoted to contemporary art?

Danielle Simonnet, a far-left member of the Paris City Council, suggested that Mr. Pinault should have just donated his collection to the state, noting the existence of another contemporary art newcomer, the Louis Vuitton Foundation.

The $143 million foundation building opened two years ago on the edge of Paris, a study in billowing sails designed by Frank Gehry and commissioned by Bernard Arnault, the chairman of LVMH, like Mr. Pinault a French luxury goods magnate and a longtime collector of contemporary art.

The rivalry between the two French billionaires dates to the so-called “handbag wars,” when they vied for control of the Italian luxury group Gucci. (Mr. Pinault emerged victorious in 2001.) They have since bought works by some of the same artists, including Mr. Hirst and Richard Serra.

In May, the Louis Vuitton Foundation tapped the conceptual artist Daniel Buren, a favorite of Mr. Pinault’s, to cover the building with a temporary rainbow of filters on thousands of panes. A spokeswoman for the foundation said it was too early to discuss whether the two institutions could cooperate — something that Mr. Pinault clearly wants to do with other large Paris museums.

Asked about any competition, Mr. Pinault demurred. “In the field of art, we don’t speak of competition,” he said. “The more places to present works, the better. Each collection is the history of a singular view.”

Still, the Louis Vuitton Foundation has set a high bar; it drew more than 1.2 million visitors last year.

Harald Falckenberg, a German industrialist and collector with a private contemporary art museum of his own outside Hamburg, Germany, said that in the rarefied universe of billionaires it did not really matter whether there was a demand for a new contemporary art institution in Paris.

“A museum is absolutely a must for a good collector,” Mr. Falckenberg said, noting that public museums could not highlight new artists in the same way as private museums because they need to appeal to visitors with mainstream, well-known art.

“Private collectors can take more risks because they are so rich,” he said. “If only 2,000 visitors come, they say it’s wonderful because they can look better at the works.”

In general, for such largess, the French state also offers generous tax deductions. Individuals can deduct 66 percent of the value of financial contributions toward art acquisitions or restoration, up to 20 percent of their income.

Mr. Pinault, the son of a farmer in Brittany, did not visit his first museum until after he was 30. Since buying a Mondrian for $8.8 million in 1991, he has intensified his collecting and now said he was building on his works from Sigmar Polke and Charles Ray while searching for new art forms from what he calls the post-internet generation.

He tends to shun big art fairs, he said, preferring to visit artists in their studios — sometimes single-handedly reviving interest in a forgotten painter such as Martial Raysse, or drawing attention to young artists such as the Danish artist Danh Vo or the French painter Claire Tabouret. Two years ago, Mr. Pinault restored a historic rectory in Lens, in the north of France, to create an annual residency program for emerging artists.

Mr. Pinault “has this appetite for risk. He doesn’t stay in his comfort zone, regarding the works he collects,” said Ms. Tabouret, who added that she was shocked when he came to her Paris gallery opening in 2013. “That compares to some people in the art world who are looking to be reassured by seeing the same look-alike works.”

Now, Mr. Pinault’s biggest challenge is what he can accomplish with a museum, which he insists is not just for the elite. Another of his advisers, Martin Bethenod, said the new art center was determined to reach beyond the core of the French capital to the banlieues, the suburbs that are concentrations of poverty and social isolation.

What does Mr. Pinault want to leave as his legacy? “By creating a museum in Paris, I do not seek to impose a trace, but to make my contribution to history,” he said. “The works of art will always have the last word.”

Correction: August 3, 2016 

An earlier version of this article misspelled the surname the chairman of LVMH. He is Bernard Arnault, not Arnaud.