We've stayed in this apartment before, Jon. Nicely appointed for a few nights & self contained, walking distance to the town square and the old castle, but we didn't have the car with us.
It says there is parking, but we didn't venture down there.
I'll pop on the place through booking.com as there are several at the bottom of the page that are owned by the same lady. Maria is the owner, and jolly nice she is too..
Carcassonne is a lovely place, too..
Good luck. Le Balcon sur le Canal du Midi