The avalanche struck around midday at the Snow Dome in the Alps' Massif des Ecrins, an easy-to-access 4,015-metre (13,170-feet) high mountain that is hugely popular with climbers.
Rescuers, backed by three helicopters and sniffer dogs, were dispatched to the scene but local official Pierre Besnard said search operations had now ended and the climbers' bodies were being transported down.
Prosecutor Raphael Balland said four of the victims were German and three were from the Czech Republic.
Another German woman was injured and was being treated in hospital, he added.
Climbers and skiers are sporadically caught in avalanches in the popular Alps, particularly during the winter season.
At least 39 people have died in snowslides this year in France, according to the National Association for the Study of Snow and Avalanches.
In January, six skiers were carried away by an avalanche in the Queyras mountain range of the Alps.
Just over two months later, two Austrians and an Italian died in the Massif des Ecrins.
But this is the most serious accident this year, and one of the deadliest over the past decade.
In 2012, a snowslide in the Mont-Blanc mountain range took the lives of nine people from Switzerland, Germany, Britain and Spain.
Christian Flagella, a member of the police force in the Hautes-Alpes region where the mountain is located, said the avalanche occurred in “winter-like conditions,” which caused a layer of snow to separate and hurtle down the hill.
Rescuer Nicolas Colombani added a lot of snow had fallen over the weekend, particularly at a high altitude.
The avalanche struck on a section of the mountain that is popular with amateur climbers as it does not require advanced technical skills.