When the gymnastics superstar Simone Biles tumbles and dances her way through her third Olympics this month, the choreography she performs in her floor routine will be seen on hundreds of millions of screens around the world.

Grégory Milan, the man who created it, still shakes his head at its reach. “I can’t quite fathom it,” he said recently at the National Institute of Sport, Expertise and Performance, or Insep, in Vincennes, a suburb of Paris, where he works as a full-time dance instructor for the French national team.

The Biles effect has brought with it something unexpected for Milan at 51: success.

Until now, Milan, a dancer and choreographer, has considered his life to be “a series of failures of sorts,” he said wryly. When he turned to gymnastics choreography full-time, in 2017, he was in debt, having started a dance company that never took off, and still reeling from the psychological scars left by a tumultuous career in ballet.

“I was furious with what I’d experienced in the dance world,” he said. “I loved the art form so much, but the behavior of the people I’d encountered in it disgusted me.”

Gymnastics has become an unlikely balm. His pure dance background is unusual in the sport: Most choreographers who work with gymnasts are also coaches and former athletes, who have an affinity for dance or have had some dance training on the side.