Emmanuel Cauchy, 58, was among a group of off-piste skiers caught up in the avalanche in the Aiguilles Rouges area around the resort of Chamonix.
A well-known figure in French mountaineering, Cauchy had written several books on mountain rescue and penned newspaper articles under the name "Doctor Vertical".
The frostbite expert founded a rescue training institute, IFREMMONT, and gave help via videolink to the team treating Elisabeth Revol, the French climber rescued from Pakistan's "killer mountain" Nanga Parbat in January.
Revol said she was "stunned" by Cauchy's death.
"The climbing world has lost its most brilliant doctor, a very great man who advanced mountain medicine by putting protocols in place for the treatment of frostbite," said Revol, who herself suffered serious frostbite in January.
Ludovic Giambiasi, the climber who planned Revol's failed ascent up the 8,125-metre (26,660-foot) Himalayan peak, expressed "immense sadness" at the news.
"Another great man that the mountain has taken from us," he told AFP from Nepal.
Spanish climbing star Kilian Jornet tweeted: "What a sad day. RIP Manu. Surely the doctor who knew the most about high mountains and altitude."
Forecaster Meteo-France had on Saturday warned of a high avalanche risk in the Alps due to unusually thick snow for this time of year, liable to collapse due to strong winds.
At least three other people were hurt in the avalanche but their injuries were not life-threatening, local mountain police said. The survivors were pulled out with the help of rescue dogs and a helicopter.
"The injured have been evacuated to the hospital in Sallanches," 30 kilometres (20 miles) away, the police said.
Three Spaniards, including a mountain guide, were killed by an avalanche while skiing off-piste in the Obers Taelli area of the Swiss Alps on Saturday.
The victims, two men aged 37 and 48 and a 38-year-old woman, were among a group of five who had taken detection equipment with them in case of an avalanche.