Novak Djokovic is having his worst season in years. At the French Open, it might not matter.

The surprising part was where the scene took place. Djokovic hadn’t yet traveled to Paris, where Roland-Garros kicked off on Sunday. He was at a fourth-tier tournament in Geneva that he had never played even a single time.

But in this strangely fitful season, Djokovic was just desperate for competitive matches.

Until last week, he had only taken the court in a tournament 17 times this year as losses piled up at a higher clip than usual. In fact, nearly halfway through the year, Djokovic has won exactly zero tournaments—despite looking untouchable after his victory at the 2023 U.S. Open. His run in Australia in January ended at the semifinal stage with a four-set loss to world No. 2 Jannik Sinner. Then he was knocked off the hard courts of the Miami Open by No. 123 Luca Nardi. And since then, Djokovic has stumbled through his clay-court campaign in fits and starts: a semifinal defeat against Casper Ruud in Monte-Carlo, a round-of-32 exit from the Italian Open.

“I just wasn’t able to find any kind of good feelings on the court, to be honest, with striking the ball," he said after losing 2-6, 3-6 to Alejandro Tabilo in Rome. “I was completely off."

That tournament was made even weirder by a bizarre incident in which a fan accidentally dropped a metal water bottle on Djokovic’s head while he was signing autographs. Though he seemed well enough the next day, showing up to the club in a bicycle helmet, he reported feeling nausea and dizziness right after the blow.

Though he reported no lingering effects, Djokovic still felt rusty and went to Geneva in the hope of finding some rhythm. There, he rattled off two quick wins before losing in the semifinal, which allowed him to set up in France in plenty of time. It wasn’t exactly how he had mapped out his spring, but no player on tour is more deliberate with how he spends his energy. Everything is designed for him to peak at the majors.

“I always strategically had a long-term plan in my head to play as long as possible so I can give my career a better chance to win more titles and break records," Djokovic said. “You know, I have arguably had the better part of my career post-30 than before 30."

Djokovic has a point. Twelve of his 24 Grand Slam titles have come since he turned 30. It’s the post-37 career that has begun to raise some questions.

Djokovic’s dip in form is just one factor contributing to this French Open men’s draw being the most open it’s been in years. For one, the twilight of 14-time champion Rafael Nadal’s career means that one of the surest things in 21st century sports is now a long shot. Sinner also arrived in Paris in less than perfect shape after dealing with a hip injury, while No. 3 Carlos Alcaraz has struggled to rediscover the kind of form that propelled him to a Wimbledon title last summer.

And yet, Djokovic remains the betting favorite to add a third title here in the space of four years to his trophy cabinet.

“It’s a crazy men’s tournament because there’s so much unpredictability at this time," said Martina Navratilova, a two-time champion at Roland-Garros and analyst for the Tennis Channel. “It’s been Novak against the field in all the majors other than the French Open. But now that Rafa is obviously not playing his best tennis, he’s the favorite even on the clay."

The women’s tournament is more clear-cut. World No. 1 Iga Swiatek, who has lifted the trophy in three of the past four editions here, once again landed in Paris head and shoulders above the rest on this surface. She won both of her high-profile clay-court tournaments in Madrid and Rome before heading to Roland-Garros, having beaten world No. 2 Aryna Sabalenka in both finals.

“Right now she looks pretty unbeatable," Navratilova said. “She is beatable, but it’s going to take a monumental effort."

But while the women’s No. 1 is in full swing, her counterpart in the men’s game knows just how much still has to happen to dominate the French Open again.

“Everything needs to be better in order for me to have at least a chance to win it," Djokovic said.

Write to Joshua Robinson at Joshua.Robinson@wsj.com