The 38-year-old Barcelona man, who has not yet been named, was descending with two other friends from the Catalan city 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 accident happened at 4.30pm when the men were coming down from the 4,015-meter peak, according to Spanish daily 20 minutos.
They had reached the peak very late, at 10pm on Saturday, the newspaper reported.
The part of the mountain traversed by the climbers is described as "long and difficult" by experts.
The climber's body was taken to the city of Grenoble while his friends were transferred by helicopter to the starting point of their expedition.
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.