Please be aware that Chamonix is becoming more and more full of ‘rich tossers’ and generally less tolerant of camping ski bums. That used to not at all be the case - this was the town for serious skiers and not only for the privileged ‘with all the bling, still not knowing a thing’. If campers cause trouble partying, breaking bottles, leaving trash etc. they will find police bothering them regularly and asking them to leave. Also the camping under the Aiguille du Midi at the Grepon is now officially forbidden - campers are asked to use official campgrounds which have showers and toilets (and are still much cheaper than renting apartments). Some people used to camp in vans at the carpark at Les Gaillands but it has strong avalanche danger and last year they used snow ploughs to create large mounds preventing vehicles from even entering that car park in winter.
On the other hand, rentals are insanely expensive now with most properties that are of decent quality going up for weekly rentals to make the owners more money to pay their insanely high mortgages ... so the town knows that they must tolerate some level of camping in order to retain restaurant and hotel workers. You will probably be more welcomed if you do get a seasonal job of some sort and can show the work contract - thus the gendarmes find that you are at least contributing to the local economy that way and may be more sympathetic.
I would be happy to see more poor ski bums in town (but wish they could still find affordable housing and not be forced to camp since a lot of them sh*t, piss and leave garbage all over the place, making it pretty damned disgusting and not mountain or enviromentally friendly!). So - please if you come, do be sure to occaisionally harass the rich tossers who frequent trendy upscale bars like ‘Le Priviledge’ or ‘No Escape’ by puking on them as they leave the establishment or the like :-) ... and definitely clean up after yourselves properly and do not destroy the area where you are camping.
BTW - it is generally more common to see seasonaires here camping in tricked out vans, proper camper vans or army surplus vehicles than in a tent ... it can get pretty cold, and it’s difficult to lock up your skis, board or other belongings if all you have is a tent. Petty theft is pretty common in winter in Chamonix.