Train to Carcassonne
Please can you tell me if there is a train link from airport to Carcassonne and if possible what their website might be?
No, there isn't a train from the airport to Carcassonne. Best bet is to take a train from Bezier to Carcassonne. See Rail Europe for more info. You don't need to make a reservation (you can buy your ticket the day you travel) but you can if you like.
To get from the airport to Bezier you can either take a taxi or shuttle.