A major rescue operation was launched following the disaster on Mont Maudit, near Chamonix, with reports that several climbers were also missing.
Christian Trommsdorff, vice president of the FGA, said: "There are three Britons among those killed."
Local media reported that the dead also included two Germans, two Swiss and two Spaniards.
It is understood 28 climbers from several countries were taking part in the expedition at the time.
Police said they were alerted at around 5.25am local time.
Several dozen gendarmes and other rescuers along with two helicopters worked to pull the dead and injured from the mountain.
The injured climbers were taken to hospital.
Mont Maudit is 4,465 metres high and part of the Mont Blanc range. It means Cursed Mountain in French.
The area is one of the most popular with climbers in the Alps.