Our advice is to bring as little as possible. If tenting, you will obviously not have the luxury of lightening your tent weight by staying indoors…you will have to rely on your own hopefully lightweight gear.
If you are taking the standard hut to hut approach, bring a medium sized backpack (35-40 liters will suffice) a few warm layers, extra socks, rain gear, a hydration system and spare water bottle for carrying extra, a light weight sleeping sack or bag liner (if you don’t bring one you will be forced to buy a cheap on in the first refuge, it is required by law, costs about 5 euros) whatever toiletries you need, sunscreen, hat and gloves, camera and electronic gear, guidebook, maps, some cash and credit card, ID/passport, some basic uh-oh gear…and little else.
Most refuges are now accepting credit cards, IF their internet connection is up, but cash (Euros) is still highly recommended.
You do not need to carry more than a few snacks. Sylvia and I carried a few packets of Gu and some pieces of bread or crackers pilfered from the breakfast cart…there will be no shortage of re-supply points on most days. There is also no need to carry a boxed or bagged lunch…you can simply stop at a refuge or café on the way.
Note that while water is plentiful, if gathered from natural sources it will need to be boiled or filtered. Livestock is roaming everywhere.
Also note that most bigger hotels in Chamonix/Les Houches will hold your luggage until you get back from the trip. The smaller gites/refuges will not do this, and at last check there are NO storage lockers of any kind in the Chamonix train station.