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Rents are heating up on one of Paris's haute avenues.

The cost of retail space along Avenue des Champs Élysées is rising as foreign tourists pour into France's capital ready to shop, European economies show glimmers of a recovery and luxury brands increasingly seek storefronts on the street.

Annual rents along the avenue, which connects the Arc de Triomphe with the Place de la Concorde, have surged 38.5% year over year to an average €13,255 ($17,770) a square meter, according to consultancy Cushman & Wakefield.

That is the highest rent increase along any of the 10 most-expensive retail locations in the world over the 12 months to the end of June, the period Cushman studied, and cements the boulevard as the third most-expensive street for retail space after Hong Kong's Causeway Bay and New York's Fifth Avenue. Rents in Causeway Bay rose 14.7% year on year to the equivalent of €24,983 per square meter and Fifth Avenue rents were flat at €20,702 per square meter.

In Europe, Champs Élysées rent far exceeds that of London's New Bond Street, where retail space fetches €8,666 a square meter.

"I'm not sure it will go much higher than this," says Christian Dubois, managing director of retail at Cushman & Wakefield in Paris. "At the end of the day, I would be very surprised if rental values would exceed this next year."

Finding an average rent for retail space on the street is difficult, brokers and investors say, because there are only a handful of deals completed each year as a result of a limited amount of space along the avenue.

One of the most eye-popping rents is MAC Cosmetics, EL -0.39%  which opened a store on the avenue this year, paying €18,000 a square meter.

"Whether that's become the new market level or not is difficult to say, but for sure [the amount tenants are prepared to pay] has been growing," says Steve Cowen, managing director of transactions at Grosvenor Fund Management Europe.

Jeweler Tiffany TIF +1.11% & Co. plans to open a store there next year, joining brands including TAG Heuer, Marks & Spencer MKS.LN +0.29% and banana republic.

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"One of the aspects of the Champs Élysées is advertising. For the luxury brands, it's a question of having their names up there," Mr. Cowen says.

Another lure for retailers is the foot traffic and how much cash the rising numbers of tourists are willing to spend, particularly wealthy Chinese visitors. The number of Chinese tourists in France rose 23.3% to 1.4 million in 2012, according to France's tourism agency DCGIS.

Paris's Champs Élysées, Rue du Faubourg Saint-Honoré, Avenue Montaigne and Rue de la Paix are four of the 10 most-expensive retail locations in Europe, according to Cushman.

"The Champs Élysées and retail high streets are benefiting from the change in nationality of tourists," said Charles Boissier, an analyst focused on Continental Europe at research firm Green Street Advisors in Paris. "The tourists that now come to Paris tend to be big spenders. Whereas before, Italian and Spanish visitors would spend more on museums, the Chinese spend more on shopping," Mr. Boissier says.

Rents also are rising on the odd-numbered side of the Champs Élysées, as more retailers move into space that was traditionally occupied by banks and restaurants, property analysts say. This is helping to close the gap between rents on the even, or "sunny side," of the two-kilometer-long avenue and the odd side.

"It's definitely the side of the street that's started to turn quickly," says Markus Meijer, chief executive of real-estate investment manager Meyer Bergman, which just bought a mixed-use property there in a joint venture with U.S. firm Thor Equities.