I can tell you what the rules in France are, and I suspect they will be similar elsewhere.
You are not allowed to CAMP in many places. But the word CAMP refers to CAR camping. I assume this is not what you mean.
Putting a little one or two man tent up somewhere up in the mountains just for the night is called a BIVOUAC. This is usually quite legal. Even in some places where you are not meant to bivouac, there is little anyone will do about it.
There is a restriction on bivouacs next to SOME gites and refuges. You have to be a minimum distnace away – out of sight is usually enough. I was challenged once when camped up above a refuge in Spain – in my very bright orange! tent, clearly visible from the refuge, but by the time the Guardian reached us we were in our sleeping bags, and not moving that night! Since we were coming down towards his refuge rather then starting from it, we were able to say we hadn’t seen the signs. He asked us to be away by 9 am the next morning, I assured him we would be gone before that, so he wished us a good night and left.
So you should not have any problems if you are out of sight of the huts.