Transportation in the Aude and Languedoc
You really do need to rent a car if you want to explore the Aude. There are car hire firms at the airport in Carcassonne as well as at train stations.
You could manage without a car but you'll miss a lot. If you're planning to stay in Carcassonne, Narbonne, or Limoux there is local bus service. There are also buses between communities but their main purpose is to take children to school and the schedules reflect it.
There are trains but once again, just between the larger towns.
Cycling is an option in some areas but in others you'd have to be a serious cyclist to tackle the hills. If you are a serious cyclist bring your own bike.
There are bike rentals shops for everyone else. One thing to keep in mind, usually the rental services only operate from June to September.