The nearest airport is Bergerac, just over an hour's drive and hire cars are readily available. Brive (Vallee de la Dordogne) airport is also an hour's drive but currently only takes Cityjet flights. Bordeaux, Limoges and Toulouse airports are all around 2 hours drive away.
Driving takes around 8 hours from Le Havre and 8.5 hours from Calais/Boulogne. Times are approximate and may vary with season. A great place to stop off if you want to split your journey is Tours, which has a wonderful medieval centre with a lively café and restaurant culture.