In reply to Adderbury Climber:
There is a massive clampdown on this at the moment with police regularly moving on vehicles that would typically have stayed in one place all season. My mate was sleeping in his van for the last month or so at GM and was moved on by the police pretty much daily. Apparently he was able to move just a few spots in the same car park but they did expect him to move his van regularly.
As others have said, it sort of depends what you mean by long-term (and also what season). For example, if you were doing the Haute Route and leaving a car for a week or so at GM that would almost certainly be fine (perhaps stick a note in the windscreen so the police know what to expect) but if you're talking months it's very likely to get towed.
https://www.chamonix.net/english/transport/parking - This site has some useful info but may not be completely up to date re the new police policy.