I am no expert on the area but did have a great visit to Carcassonne, Collioure and wonderful Villefranche de Conflent back in 2018. We stopped briefly in Toulouse on the way to Carcassonne. We stopped overnight in Toulouse after taking the Little Yellow Train from Villefranche de Conflent to Latour de Carol then just catching the Barcelona to Toulouse train with minutes to spare. Wouldn't have cared if we missed it as Latour de Carol would've been worth a look.
This may not be of interest to you but I'll put it out there anyway.
We spent several days in each of Carcassonne, Collioure and Villefranche de Conflent but would've liked to spend longer in each.
Toulouse was not of any great interest to us.
In Carcassonne we stayed in the actual town, it's really nice and well worth some time. Most RS tourists seem to just want a flying visit to the Cite' and usually stay within. We were happy to be staying among the locals in town, we do a tight budget so it wasn't really a choice but glad we did. We visited the Cite' in the evening, early morning around sunrise and middle of the day. It was crowded in the middle of the day.
The town itself wasn't at all crowded except the day the Tour de France finished there. That was a bonus standing at the finish line as they came through then mingling with the riders afterwards.
Collioure was pretty busy, it was July so not surprising. Beautiful spot. Each morning I was up in time for a swim before the sun popped up above the Mediterranean horizon. Then a run up past the ancient windmill through vinyards to the spectacular hillside Fort. A few more swims on the return leg. If you like walking, interesting architecture and people watching and nature then Collioure is ideal. We had breakfast each morning in the Templiers Bar, amazing art collection.
Villefranche de Conflent is a tiny walled village with a hilltop fort accessible by stairs through tunnels. This little village probably topped the favourite list for both myself and my wife. Also has some interesting caves near town. We got there by train from Collioure to Perpignan the a bus the rest of the way. I think the train is now back running though.
From V.d C. we caught the Little Yellow Train sitting in an open top carriage as a wound it's way very slowly through the Pyrenees. Great fun, a bit of a change up from the 320 kph intercities. As I said this meets up with the Barcelona/ Toulouse line at Latour.
We loved this part of our French trip.