We almost did not come here but so glad we did! September is definitely low traffic season and there is actually a bit of space between other visitors of the cité. Lots of shops within the cité walls selling all sorts of medieval looking goods, artists for wall art and sculptures, and restaurants. The citadel sees about 4 million visitors annually. It is a citadel because it protects a city as well, so it is not just a castle.
We camped at Camping à la Cité which is a municipal campground. Supposedly a 4-star campground that says it does not need to provide for toilet paper and charges for wifi. Yet it is a 20 minute stroll to see Carcassonne from there so we still camped there. You probably can get away with wild camping if you hide well enough by the trail beside the stream by setting up at night and tearing down at dawn and sneaking into the campground for a shower.