There is a regional, slow train from Avignon Centre, the train station just outside the city walls, that stops near the Marseille Provence airport. No reservations. A five-minute shuttle ride connects to the airport terminal. Or the TGV service from the high-speed train station outside Avignon whisks you to the Aix TGV and there is a shuttle bus from there to the airport. It is shown on the SNCF site as taking about a half hour. Sorry, as I am typing this the SNCF site is partially out-of-order (mon Dieu!) so I can't give you the exact links.
http://www.marseille-airport.com/ For information about the airport.