Traveling independent from MRS to Quai de l’Oulle, Avignon. What are best options for transfer?
Just take the train from the airport to Avignon and then it's either walk or taxi. Trains are frequent and take about an hour.
Note that the station is some distance from Marseille airport and you need to get a shuttle bus from outside the terminal.
The Marseille Provence airport has a useful Internet site that will diagram your route from the airport to Avignon.
https://www.marseille-airport.com/access-car-parks/access/trains
The five-minute shuttle to the local station puts you on a regional train that is slow and does not provide seat reservations. But it stops conveniently at one entrance to the old walled city.