The 38-year-old man, who has not yet been named, was descending with three friends on a snowy part of Col des Ecrins, on the northwest side of the Dome des Ecrins, when he fell a few hundred metres.
The part of the mountain traversed by the climbers is described as "long and difficult" by experts.
The incident follows the death of a Russian climber and the serious injury of another on Friday after the pair fell several hundred metres on Mount Blanc.