There is a TGV service that runs to Carcassonne, either from Toulouse or from Narbonne but there is not yet a high-speed line so the journey times are somewhat slower than you might expect. There is a new high-speed line (LGV – Ligne à Grande Vitesse) running between Paris and Bordeaux (two hours), from where you can take a train to Toulouse (and sometimes direct to Carcassonne). There is also a TGV service running from Paris via Lyon and Beziers, where you can change for Narbonne (and sometimes direct to Carcassonne).
There are three websites worth consulting if you are considering this option:
SNCF (the French national railway company)