Getting to Centre Les Labadous by car is no problem, since all navigation devices find Les Labadous. Follow signs from the town of Couiza (in the Aude valley): Centre Les Labadous is just below Rennes-le-Château, the village perched on the hilltop.
The closest airports are Carcassonne and Perpignan, but Toulouse-Blagnac offers many more flights. From Toulouse to Les Labadous is ca. 2 hours by car, from Carcassonne it’s an hour.
Public transportation will get you from the airport to Couiza, a small town in the Aude valley, some 7 km from Les Labadous. While you can reach Les Labadous by taxi, it is certainly advantageous to rent a car, also to reach shops, restaurants, banks, etc.