The accident occurred on Saturday near the Pic de Pinede summit in the Cirque d'Estaube.
His hiking partner was out of range to make telephone contact and descended to the Spanish side to raise the alert.
Rescue workers found the body of the young man, who died on the spot after a fall of 150 to 200 metres from an altitude of 2,860 metres (9,440 feet), a police officer said.
The body was winched up by a helicopter, he said.
The news comes just days after four French climbers lost their lives in two separate incidents on Mont Blanc.
Europe's highest peak is crawling with climbers during the summer months, and at least 12 people are known to have died on the mountain since the climbing season began, which tops out at 4,810 metres.