The accident occurred at 4 a.m. on Mont Blanc du Tacul, a 14,000-foot (4,248 meter) peak that is one of the most popular routes to the summit of Mont Blanc, western Europe's highest peak at 15,782 feet (4,810 meters).
The injured climber was evacuated to a hospital in nearby Annecy, 25 miles (40 kilometers) south of Geneva, Switzerland.
The mountain search and rescue service in Chamonix said that bad weather prevented them initially from using helicopters to reach the site of the accident.
Stuart Macdonald, a British mountain guide and director of the Avalanche Academy in Chamonix, said the slope where the accident occurred is prone to avalanches owing to its steep 30- to 40-degree inclination, and it has a reputation as a place to be avoided after heavy snow.
About a week had passed since the last heavy snowfall in the area, which is generally enough time to permit a resumption of climbing, Macdonald said.
The route "can be very crowded" this time of year, Macdonald said, with between 30 and 50 climbers on the slope at the time the accident occurred.
Two more climbers were found dead Tuesday morning by rescuers in an Alpine area about 80 miles (130 kilometers) southwest of the accident on Mont Blanc, said Capt. Laurent Jaunatre, who is with a division of the Alpine police based in Grenoble.
He said the French man and woman, both in their 50s, set off early Monday morning up the Roche de la Muzelle mountain. They were last spotted at noon that day when they were beginning their descent, and an alert was sent out when they did not return in the evening.
Rescue teams began a ground search that night and found the couple early Tuesday with the use of a helicopter. It is unclear how they died.
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