There are high speed trains from Paris several times a day to Narbonne where you will find the usual car rental offices. It is then an easy 40 minute drive to La Rassada. You can also get a high speed train from Barcelona to Perpignan, (also an easy 40 minute drive to get here).
From the UK you can also take the train from London to Narbonne via Lille or Paris.
More info on all train journeys available on the SNCF website in English.
The nearest airports are Perpignan (40min); Béziers (1h); Carcassonne (1h30); Montpellier (1h30); Toulouse (1h45); and on the Spanish side of the border you also have the option to fly into/out of Girona (1h45) or Barcelona (2h45).
All have low cost flights from the UK with Ryanair, EasyJet or Flybe. Car rental is also available from all these airports (N.B some companies charge extra when booking a car from Spain if you are coming into France).