"The news was confirmed to me by family members," said the federation's president Bernard Amsalem.
49-year-old Quinon won gold in the 1984 Los Angeles Olympic Games, a year after breaking the world record with a jump of 5.82 metres.
According to a source quoted by AFP and reported in local newspaper Var Matin, "he jumped head first through a window from a height of five metres."
"He was depressed, he'd been taking pills and was not himself," the source said.
Fellow Olympic pole-vaulting champion Jean Galfione, who won gold at the Atlanta Olympics in 1996, told newspaper Libération he had seen Quinon a month ago.
"He was a sensitive person. He'd been going through a difficult period," he said. "We knew he could be excessive, particularly when it concerned himself."
Quinon's success at the Los Angeles games was the first time a Frenchman had won Olympic gold in the event. After a series of injuries he eventually retired in 1992.
After retirement, he moved to the town of Hyères on the Mediterranean coast where he opened a restaurant. He had recently been involved with preparations for the 2015 World Masters Athletics in Lyon.