Avignon to Marseille

I think you are out of luck for Sunday, unless you drive. Even staying overnight Saturday in Marseilles will entail a cab to get to the airport in time to make a 6AM flight. So you might want to stay at a hotel near the airport. To get to Marseilles without a car, take the train.

You can easily take the train from either Avignon Centre or Avignon TGV to Marseille-St. Charles. If you book from Avignon Centre, they will most likely bus you to Avignon TGV. The trip takes 1hr to 1hr30min. The runs with the bus are the shortest. Fare is 19.40E. Once in Marseille, I suggest staying at the airport. 6:00am is a very early flight. Here's a LINK to a list of airport hotels. See which ones have shuttles to the airport. You have no chance of trying this early on a Sunday morning. The first train out of Avignon departs at 5:46

Are you booked through on one ticket from Marseille to CDG and then from CDG home? If not, consider cancelling your flight from Marseille to CDG and take a direct TGV from Avignon to CDG on Saturday evening, departing at 18:52 and arriving at 22:02. Spend the night in a hotel near CDG.

You can take a regional train from Avignon Centre, rather than going out to Avignon TGV. On the www.tgv-europe.com site, specify your destination as MARSEILLE PROVENCE AEROPORT. The result will show a local train plus a connection between the (very small) station and the airport itself but it is only a shuttle bus taking a few minutes. The regional trains are far less comfortable than TGV but the elapsed time, once the shuttles are considered, won't be much different. With TGV you will have to take not only the bus to Avignon TGV but also a longer shuttle to the airport from either Aix or the St-Charles station in the city. That terminal is not one of the SNCF's happier achievements.
Anyhow, such an early departure dooms you to staying somewhere close to the airport and I cannot help with neighbouring hotels.