If you don't need to collect a car at the airport, car rental is available with Avis from its office opposite the train station.
Driving in central Carcassonne is straightforward, with the roads largely arranged in a grid pattern. Most of the roads are one way, but they are quite easy to navigate around.
The new town is encircled by the D119, the N113 and Boulevard Marcou. The N113 then runs southeast across the River Aude, with a number of smaller roads running of it up to the historic Cité with its imposing fortress. Note that cars are banned from the streets of the Cité from 10am to 6pm daily.
As Carcassonne is relatively small, traffic doesn’t tend to be too heavy except in rush hour periods. In the summer, however, the streets to and from the Cité can get very busy, especially with coaches, and drivers can be quite impatient as a result.
There are three car parks close to the medieval city, all of which require a steep walk up the hill to reach the fortress. There are a number of underground car parks in the ville basse, and you can often find free, on-street parking on Quai Bellevue (across the river from the Cité).