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Carcassonne has two out of town shopping areas, one to the east and one to the west (by the airport).
Both have large supermarkets and all the major chains of shops can be found in one or the other. The West shopping is much bigger and should service all your needs. The Geant supermarket there is huge and has everything.
Supermarkets are not the best place to buy good local wine. Carcassone has an excellent specialist that sells at prices close to the growers. It is La Passion du Vin at 35 avenue Franklin Roosevelt, just off the inner ring of Carcassonne. Highly recommended for wines from all the region’s appellations. For more on wine, see here.
Carcassonne has a market on Tuesday, Thursday and Saturday morning. The excellent food market is in Place Carnot and there is also a touristy flea market outside the centre (to the west of the town walls). Almost every town has a market so there is plenty of opportunity to indulge yourself in the fresh produce of the region. List (not checked) here.
There is a very pleasant golf course just ten minutes by car from Au Berg. It is Golf Club de Carcassonne and is situated in the grounds of the rather grand four star hotel Domaine d’Auriac.
If you fancy a lesson, the pros are very good (Both speak English and French) and there is a driving range at which you only pay for the balls (€2 per bucket). You can rent reasonable clubs at the pro shop.