Follow the A20 to Luchon all the way from Calais. You could break up the journey with a night or lunch in Orleans or Bourges. Luchon is only 20km from the Château.
Trains run twice daily to nearby towns of St Gaudens and Luchon.
Toulouse Airport is the closest large airport, about 1 hour 20 from the Château. From there you can catch regular flights from across the UK. Tarbes/Lourdes Airport is only 45 minutes away, where you can get twice weekly flights from London Stansted and Paris.