In reply to mollygarbs:
Personally I would start from Argentiere and go up Aiguillette de Poset, over the Col de Balme and camp in the site at the top of Trient. It is a semi official site with a toilet, water and a covered eating area.
The next day you can either go over the Fenetre d'Arpette or for an easier day on the Bovine route to Champex where there is a small camp site on the entrance to the village.
Following day to the camp site in La Fouly and then over the Grand col Ferret into Italy. You will either need to look for a refuge or be imaginative at the end of Val Ferret. The balcon past the Refs Bonatti & Bertone is one of the best days on the trip with stunning views of the S face of the Mont Blanc massive. It is possible to cut down to the camp site at Planpincieux but it leaves you with a dilemma for the following day unless you take a bus to the end of Val Veny and walk over the col and down to La Chapieux where there is a semi wild camp as well as an Auberge.
Once over the Col de Croix de Bonhomme/Col de Bonhomme it is downhill to a bivouac by the Ref de la Baume or continue to a camp site in Les Contamine.
The high route via Chalet de Miage is really stunning but tough and you will end up in Les Houches. Not sure if there is a camp site in Les Houches but many people take the bus to a site in Chamonix and then come back the next day to walk up past the animal park and ref Bellachat. There are several wild camp site above the refuge and before Le Brevant.
Over Le Brevant, Flegere and down to the col de Montet ends the circuit.
Now this is only a brief idea of the possibilities as it can be shortened by using public transport/lofts etc or lengthened depending on the amount of time you have,
I suggest that you factor in a couple of rest days if you are not in a great hurry.
Hope this helps.
Mike