I like Europcar...but if you have a favourite company form the US (Hertz, Avis etc), they are mostly all represented the TGV staion in Avignon.

Reserve your car in advance through AutoEurope (noted above) or Kemwel its sister company, both American brokers situated in Maine. Do not just reserve via web. Call and speak with an agent and ask whether there are any discounts/specials available. They will shop for you among the local companies and will get you the best deal. If you find a better deal on your own, they will match the price. The best part is service: should something happen during or following your trip, they have an excellent customer service department and they speak English.