The Tour du Mont Blanc travels through France, Switzerland and Italy.
If you are a member of one of the respective alpine clubs, you get discount on accommodation at their mountain huts. Unless you plan to stay exclusively in alpine club mountain huts, it is not usually worthwhile getting membership only for the hike. Here are the details on each alpine club membership:
FRENCH ALPINE CLUB MEMBERSHIP
The French Alpine Club has a membership program that provides discounts to their mountain huts. Membership is about 100 - 120€ and is open to non-French citizens. For full details click here. The huts along the Tour du Mont Blanc that are owned by the French Alpine Club include Albert Premier (1er), Refuge Croix du Bonhomme and Chalet Des Contamines.
SWISS ALPINE CLUB MEMBERSHIP
The Swiss Alpine Club has a membership program that provides discounts to their mountain huts. Membership is from 80 CHF and is open to non-Swiss citizens. For full details click here. None of the huts along the Tour du Mont Blanc are owned by the Swiss Alpine Club.
ITALIAN ALPINE CLUB MEMBERSHIP
The Italian Alpine Club has a membership program that provides discounts to their mountain huts. Membership is from 45€ and is open to non-Italian citizens. For full details click here. The huts along the Tour du Mont Blanc that are owned by the Italian Alpine Club are Rifugio Elisabetta and Rifugio Monte Bianco (in Val Veny off the TMB trail)