Marseilles to Avignon

Sure, train - one change. About 45 mins. Taking a Viking tour?

The airport website http://www.marseille-airport.com/access-car-parks/access/by-train-or-by-bus gives a schedule for the train to Avignon.

That's one of the few route segments on the train where I find that tickets are checked relatively often, because there are a lot of people playing hop-on hop-off free-riding, so be sure to have a valid stamped ticket handy.

That link to the Marseille airport is useful; the railroad itself can be seen at http://en.voyages-sncf.com/en/

You can choose between the high-speed TGV and the slow regional train. The TGV requires a shuttle bus ride of about 10 minutes to the TGV station on the outskirts of Aix-en-Provence. The Avignon TGV station is also on the outskirts with a 5-minute train to the old station in the city. The regional train station near the Marseille airport is a five-minute shuttle bus ride from the front door and its regional train arrives in Avignon's old station at the main gate to the walled city.

The destinations on the SNCF screen are a little tricky. For the local train, you choose to depart Marseille Provence Aeroport for Avignon Centre and the screen will show there is one transfer. But that connection refers to the five-minute bus ride, part of the ticket, to the Vitrolles Aeroport Marseille Provence train station, as the local stop is formally known.
Similarly the bus to Aix-en-Provence shows as one change on the SNCF schedule. The TGV train needs a seat reservation but is a lot sleeker than the regional train, which can rattle as it rolls but puts you down closer to the heart of Avignon.