Here is a list of hotels in the town of Carcassonne. As the airport isn't far from Carcassonne you should be able to get to any of the hotels below easy enough.
Domaine D'auriac
Hôtel De La Cité
Best Western Le Donjon
Hôtel du Soleil Le Terminus
Mercure Carcassonne Porte De La Cite
Au Royal Hotel
Inter-Hotel Espace Cite
Hôtel Bosquet Carcassonne
Fasthotel
Hôtel Balladins Carcassonne
Village Pour Tous - Gît'Ôstal
Premiere Classe Carcassonne
Appart'city Cap Affaires Carcassonne
Citea Barbacane
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This website has no relationship whatsoever with the Carcassonne Airport.