If you have a GPS you can drive by night too. Without – i would do what you wrote. Stay at the Airport and pick up the car in the morning. I hardly speak french and when we arrive i really felt lost. My Austrian Mobilephone Operator didn’t work over there and my credit cards got rejected for whatever reason at the airport :O. If you speak french that should be fine.
If you want to live near to the kite beach you should try http://cases-mabouya.com/. This is near Ponte Faula – the main kitespot. From this appartement, i think you can walk to the beach…
Have fun, Martinique is really a beautiful place to stay!