If you really want peace and quiet and no facilities at all, there are two places to camp on the road up to the Cirque de Troumouse, near Héas.
"Camping a la Ferme Chez Ernest" and a small camping situated near to the hamlet of Héas. Small pleasant café/restaurant.
In reply to Palomino1hills:
I recommend the campsite at Le Pla, midway between Mijanes and Querigut. We discovered it one summer when trying to escape the heat of Narbonne. I still remember waking to the sound of birdsong in the beautiful mixed woodland of the Donezan. And you get to cycle up the Port the same way that the Tour has done in recent years.
There are other great cycle routes in the area, including a circuit taking in the col de Jau.
There's a lovely, if popular, walk up to the Lac de Laurenti that you can do from the site, too.
It is on the other side of the Port de Pailheres from Ax les Thermes, however.