The body of Julien Gruss, 29, was found in the Cuneo province of north-west Italy, La Stampa reported.
Gruss' sister raised the alarm after he failed to return from his off-piste skiing holiday, the newspaper said. Early reports suggest that the Frenchman fell and hit his head on rocks, although a police investigation into the cause of death has been opened.
The news came the same morning that the body of a second French man was found in Italy’s Piedmont region.
The alpine skier, whose name has not yet been released, was on the descent from the Gran Paradiso mountain when he is thought to have fallen. He hit a sheet of ice while skiing with a friend, who went to a refuge to call for help after being unable to find his companion, Corriere della Sera said.
Just two days earlier, an Italian teenager died on the Italy-France border while skiing with friends. Riccardo Capitanio, 15, was overwhelmed by an avalanche on Sunday close to Claviere, La Stampa reported.
Another accident struck the border region on Friday, when a 24-year-old French snowboarder was killed in an avalanche. On the same day, a 50-year-old man, the guard of a mountain shelter, died after being swept away by a mass of snow.
Since Christmas three people have also been killed in avalanches in the Swiss Alps.