In reply to srah:
I haven't heard reports of conditions this season in the Vanoise, so can only generalise from past experience, but usually by the end of June most of the balcon sections will be clear. The Col de la Vanoise and the Col de Chaviere may well still have extensive snowfields, but they're mostly low-gradient. You won't see many French walkers with axes. But the north side of the Col d'Aussois, if you should choose to go that way, is quite a long steepish snowfield with rock-and-boulder runouts, and I've been glad of the reassurance of an axe going down there at this point in the season. It partly depends on your party - if you've limited experience of alpine snow I'd be inclined to avoid crossing the Aussois in that direction.
You could try ringing the Nat Park information office or the Bureau des Guides in Pralognan, but I've found them rather reluctant to give advice when they can't judge your competence - understandably they tend to err on the side of caution.
Hope you get great weather, it's a superb tour.