The 47-year-old ski instructor and his 59-year-old client had left Avoriaz, on the French side, to ski towards the Col de Cou near Les Crosets, when the snow-laden ledge they were standing on gave way beneath them, Valais cantonal police said.
The pair fell 100 metres down a cliff.
Emergency services were alerted by another skier who found a ski belonging to one of the Frenchmen in the off-piste area.
Despite the efforts of rescue workers and a French doctor to revive the men, both died at the scene.
Heavy snowfall in recent days has meant a risk of avalanches in many parts of Switzerland.
Several people have died in incidents this winter season, particularly off-piste skiers.