A great place to spend a few hours is Lac de la Cavayere . You can take your Carcassonne car rental out there or you may prefer the option of a bus (the number seven from Square Gambetta).
Walking in Lac de la Cavayere
You should be able to do a full walk around the lake in less than an hour or so if moving at a brisk pace.
There is much to admire and take in as you move along. In the centre you will find a bird reserve.
You can find more information about the various attractions in and around this area here.