Travel Barcelona to Avignon

Have you considered taking the train or flying from Barcelona - Marseilles?

That's over 400 Km, so I doubt you will find an economical car service, if you can find one at all. It's easy enough by train, but it should get even easier when direct high speed trains start running between Barcelona and various locations in France. Spanish AVE trains going to Marseilles will probably be the best bet, but they haven't started yet and the schedules haven't been announced. See this page on The Man in Seat 61 (3rd news item at the time of writing) and keep checking back there for updates: http://www.seat61.com/news.htm

Another option is to fly Iberia or Vueling from Barcelona to Marseille, the nearest airport to Avignon. Compare prices and time with the train to make your choice.

To find flights, use http://www.skyscanner.com/. Fares on Vueling should not have any penalty for one way travel, but Iberia may be much higher for one way than for round trip. If this is the case, you can buy a round trip ticket and just discard the second half. Don't discard the first half, as the airline will cancel the second half. If you're going to need a rental car in France, you could also consider taking the train from Barcelona to a closer point in France (say, Perpignan) and renting a car there. Cars rented and returned in the same country, even in different cities, usually have no additional drop off fee. However, be aware that for 6 people plus their luggage, you'll need two cars (or something much larger than a standard car, which will be hard to maneuver on small roads).