The last on our list.
Ryanair flies Stansted (& other European cities) to Carcassonne. There is a shuttle (€5) that meets all incoming planes provides for outgoing planes, and runs direct from the airport to Carcassonne rail station. There you can catch the €1 train/ bus connection to Limoux or Couiza as described above.
From other locations you may need to fly to Toulouse, Beziers or Barcelona and then
train/ coach on.