If you are driving, the nearest ports are Caen, St Malo, Cherbourg and Roscoff. It is around 9 hours driving from any of these and, taking ferry arrival/departure times into account, you should allow for an overnight stop en-route from the channel port to the centre. Brittany ferries sail from Plymouth and Portsmouth to these ports.
Coming by train, you can take the Eurostar Paris connection. TGV trains from Paris to Toulouse come via Bordeux. If you come via Paris you must change trains and stations in Paris, for which you should allow 90 minutes. If you change trains at Lille (on the way to Paris), it is only a platform change, which is a lot easier, but the fare is quite a bit more expensive. In Toulouse you change onto the train which comes to Pamiers and goes on to Foix, Ax-les-Thermes and then to the border with Andorra. From many parts of England and Wales it is possible to do the complete journey in a day, if you’re prepared to start early. For options visit European Rail or seat61.
Flights to Carcassonne using Ryanair are available from : Liverpool, East Midlands, London Stansted, Glasgow International, Edinburgh, Dublin, Cork
Flights to Toulouse using EasyJet are available from Bristol, London Gatwick, Paris CDG, Paris Orly
Flights to Toulouse using Jet2 are available from Manchester
British Airways, Air France, Aer Lingus, KLM also fly into Toulouse from London or various regional airports.
Not all flights are all year round.