The cable cars got stuck at 3:40pm (1340 GMT) Thursday at an altitude of 3,800 metres (12,500 feet) in the French Alps after an unexplained technical incident, initially with 110 people on board.
Seventy-seven people were evacuated through the evening, including 48 who were airlifted out by helicopter and around 30 travelling in cars closest to the ground who were able to climb down with the help of rescuers.
The remaining tourists were forced to spend the night dangling in mid-air at high altitude and in deteriorating weather conditions after the rescue operation was suspended at nightfall.
They were rescued on Friday morning when the operation recommenced.
"We were forced to stop rescue operations at 8:45pm" for safety reasons, the dark and the weather making it too dangerous, the prefect of the Haute-Savoie region, Georges François Leclerc said, adding that they were not able to "guarantee the safety of the pilots, rescuers and the people stuck in the cars". He described the operation as "very difficult".
Twelve people were evacuated by Italian rescuers after the French operation had stopped, and during the night, a team of five rescuers, three French and two Italian police officers also attempted to reach the trapped tourists.
They were given special survival kits including energy bars and emergency blankets. Specialist rescuers spent the night in some of the cabins, including the one where the 10-year-old child was to try to reassure the tourists.
However one cluster of cabins could not be reached and the occupants had to spend the night alone.
“We were in contact with them throughout the night; they were cold but there was no vital distress,” said Stephane Bozon from the specialist mountain military police in Chamonix.
The incident was caused by cables that got crossed for "unknown reasons", but a gust of wind is thought to have played a part, Mathieu Dechavanne, CEO of the Mont-Blanc Company that manages the cable cars, told AFP.
The employees of the company were not able to repair the cars, forcing an evacuation operation to begin around 5:00pm. The cable cars connect Aiguille du Midi on the French side of the mountains with Pointe Helbronner on the Italian border, where the rescued passengers were taken.
Weather conditions were at first good but later deteriorated turning cloudy at the high altitudes.
"The last hour was very, very long. We called the (Mont-Blanc) company, who explained to us that three cables had become tangled and there was only one left to un-cross but they weren't able to do it," a tourist told local radio station France Bleu Pays de Savoie.
"They tried to evacuate us but it was very difficult. I had to close my eyes for a good while and try to think about something else," he added.
The rescue operation involved four helicopters from France and Italy.
The cable cars, which carry four passengers each, offer panoramic views of Mont Blanc, which straddles the French-Italian border.
The cars were restarted early on Friday morning, the operators said, while the remaining passengers were rescued without the use of helicopters.
"It restarted five minutes ago, the last cable (which was blocking the system) was untangled," Mathieu Dechavanne, the head of the operating company said just before 8am (0600 GMT).
The incident comes five years after around 40 people were stuck for nearly seven hours on the Grande-Motte cable car in the southeastern French Alps after it broke down. They were evacuated through trap doors in the floor of the cars, using ropes to reach the ground 40 metres (130 feet) below.anc