A local police official, speaking under condition of anonymity, said the 110 people were trapped in the Vallee Blanche cable car.
It rises to an altitude of 12,395 feet and connects the famed Aiguille du Midi peak to the Pointe Helbronner.
The mayor of Chamonix, Eric Fournier, said the people were being evacuated by helicopter from the Mont Blanc massif in the Alps.
Mr Fournier added: “There’s nothing fundamentally to fear.”
Italian and French authorities are helping with the rescue but it was not yet clear why the cable car stopped working.