I hike in that very area some years ago. We would typically get water from the refuges.
Le refuge de la Balme
Le refuge de la croix du Bonhomme
Le refuge des Mottets
Il refugio Elisabetta
You'll find clean water there, and they are not that far apart (about half a day between each, I'd say).
The rest of the time, if you don't have enough ...
Probably your best solution is to take a small camping stove and boil water you get from a creek. The huts are basically doing the same when they sell you tea water.
In my experience, most bivoucs require you to bring your own stove anyways, so this method hardly adds any weight (maybe some extra gas). It is way cheaper than buying a water filter and it does ...
Before drinking from a stream, check your map to see where that stream comes from.
Does it flow through a settlement or even worse past something industrial? Does it come from a lake? Could be polluted with anything, including things you might not be able to get rid of by filtering or cooking. If you have a choice, avoid! (if this is a survival situation: ...