Four helicopters had managed to rescue 65 people from the cable cars before night fell over the Alps, Interior Minister Bernard Cazeneuve said in a statement.
The 5-km (3-mile) ride between the Aiguille du Midi peak and the Helbronner summit, at the border between France and Italy, is at an altitude of over 3,000 metres (9,840 feet). It usually takes 35 minutes but has been stuck since 5:30pm (1530 GMT).
France 3 TV said the cable cars stopped when cables became tangled in high winds. Cazeneuve mentioned a technical incident but gave no details.
Blankets and food were delivered by helicopters to those still stuck inside. Rescue workers would stay with them overnight.