PARIS—If Novak Djokovic wins his first French Open title this year, he’ll likely celebrate long and hard. But he’s not going to order a steak. Djokovic, perhaps the world’s most famous practitioner of a gluten-free diet, confirmed on Thursday that he no longer eats meat, either.

Djokovic, who won his second-round match at the French Open on Thursday, said he has been a “pescatarian” for almost a year now. “Vegan with eating a little bit of fish here and there,” he said.

In 2010, Djokovic learned that he was allergic to gluten and cut it out of his diet. He had an otherworldly season in 2011 and has been the world’s most consistent player since. His devotion to his diet has only gotten stronger. Earlier this spring, he opened a vegan restaurant in Monte Carlo, where he lives.

Djokovic, the top-ranked player in the world, is the favorite to win his first French Open. His 7-5, 6-3, 6-4 victory over Steve Darcis on Thursday puts him in the third round. The French Open is the only Grand Slam tournament Djokovic has not won.

In other matches in Paris on Thursday, Rafael Nadal and Serena Williams both advanced with easy victories. Venus Williams beat fellow American Louisa Chirico, a 20-year-old who had an excellent clay-court season and came through the qualifying tournament to earn a spot in the French Open. Madison Keys, also playing well on clay, advanced to the third round, too.