Searching for a solution, he last month replaced his old coach with Amélie Mauresmo, the 39-year-old former pro who is a hero in France because of her pair of Grand Slam singles titles and because she is the last French player, male of female, to reach world No. 1.

Other top male players are coached by a woman, but those female coaches are relatives. Pouille’s arrangement with Mauresmo continues to be a story line, even though Mauresmo has coached men before, notably Britain’s Andy Murray, whom she guided to the Melbourne final in 2015.

“Men are coaching women, so why not the contrary?” Pouille said at his news conference. “It’s not about being a man or a woman, it’s about knowing tennis, about having the good state of mind.”

He summed up the ways that Mauresmo has helped him turn a corner. She creates “a cool atmosphere,” he explained. “We’re not too serious. We can laugh. We can make jokes. Once we go and hit the balls, we are really into it.”

In other words, balance.

And more: “I think she’s bringing a lot of confidence to my game.”

Pouille will need every ounce of cool confidence, and likely the best tennis of his life, if he is to beat Djokovic on a packed center court stadium Friday.

Will Pouille be overlooked once again?

Not a chance, said Djokovic. “I always thought he’s a great player,” the Serb told the assembled reporters in the wake of his own quarterfinal win.

Pouille “deserves to be definitely at the top 15, maybe top 10 of the world,” Djokovic added. “He’s got that quality and potential, no question about it. Here we go. It’s the semifinals. We both want to get to the finals. Hopefully we can both be fresh and fit and put on the great show.”