Although heli-skiing is not permitted in France, due to Chamonix’s proximity to Italy & Switzerland it is possible to arrange a day’s heli-skiing over the border.
There is an enormous range of off-piste and back-country skiing in the Chamonix ski area including the famous Vallee Blanche itinerary for which you do need a guide. Most of the ski hire shops have touring skis and off-piste equipment available for hire.