Mountain guides confirmed that Adèle Milloz, 26, and her climbing partner, 30, fell to their death on Friday before 6.15pm on the route to Aiguille du Peigne.
The climbers were over 10,000ft up, crossing Aiguille du Peigne to Aiguille du Midi.
Other mountaineers saw the two fall and called for help. They then stopped their own climb due to shock and were lifted off the mountain.
Ms Milloz had grown up in Tignes, in the Alps, and won gold in individual and team sprint ski mountaineering at the Winter Military World Games in Sochi five years ago.
She had retired from competitive sport and was training to become a mountaineering guide.
The circumstances around the fall are unknown and an investigation is underway.
Amélie Oudéa-Castéra, the French minister for sports and the Olympics tweeted a tribute to Ms Milloz.
She said: “Deeply saddened by the death of ski mountaineering champion Adèle Milloz in Mont Blanc, at the age of 26, and of the woman who was by her side.
“I extend my deepest condolences to her family, loved ones and her colleagues from the National School of Skiing and Mountaineering in Chamonix.”
The Mont Blanc summit is known to be perilous, in particular, the Goûter route from Saint-Gervais-les-Bains which takes climbers to the top of the highest peak in western Europe.
Earlier this month, Jean-Marc Peillex, mayor of the town, said mountaineers trekking up the summit will have to pay out €15,000 (£12,600) to cover costs for their own rescue missions if they get stranded or die.
It comes after the route was reported extremely dry, leading to large amounts of rockfall creating dangerous conditions for climbers.
More than 100 people are reported to have died on the route in the past 20 years.