Flying

The Château is ideally positioned between 3 international and 1 domestic airports.

Bergerac Airport is 50min drive. Serviced by Ryanair and Flybe.
Toulouse Airport & Bordeaux Airport are equidistant of 1hr 30 mins drive - both large International Airport with many international carriers.
Agen Airport is just 20min drive. It is a small domestic airport if connecting from Paris (with Hop!) or with your own aircraft. (From Paris, consider taking the TGV.)

Driving

Following this GoogleMaps link is easiest and most reliable! (But please use the OTHER drive to enter the Château, rather than the one that Maps route you to.)

If using your car SatNav, please input "Laugnac". The Château is about 5 minutes South of Laugnac village on D13. 
Do NOT input "Lasfargues", it is another village 40 min away! (This is a common mistake.)

Enter via the SOUTHERN entrance, identifiable afar by the very tall cedar trees on both sides of the avenue. Enter between the stone pillars with a name plaque (see photo below). The Château will reveal itself as you drive down the drive! 

Note that GoogleMaps will route to the Northern drive / back entrance, which has a street sign and a metal cross at the entry on the D13 road immediately adjacent to a big bend in the road. AVOID this entry as this is the service entrance and, most importantly, you will miss the magical tree-lined avenue!!

Trains / TGV

Agen train station is just 20 minutes drive, providing easy access to the TGV and train network.
From here you can reach Bordeaux, Toulouse, Montpellier or even Paris for a day-trip!  
Sixt and Europcar have an office here for car rental, but ensure you book well in advance! 

Taxis

You should not rely entirely on taxi services to reach the château and for the duration of your stay, largely due to their cost and scarcity.
It is strongly recommended that you hire a car from airport or train station to reach the Château. This will give you the flexibility you will need to access the shops, transportation, restaurants etc.
If you do require a taxi you will need to book in advance, and almost always, the meter will be switched on from their origination point (not your pick up point).