Flight
Both airports work and then you can either take another flight to the Bordeaux airport or train (about 3 hours by train and 1.15 hour by flight)
Train
If you're taking the train from the airport, it takes about 3 hours train to Bordeaux, and the Chateau is a 20min car ride from the train station
Flight
Or you can fly to Bordeaux–Mérignac Airport! whichever is more convenient/affordable.