Realistic South of France itinerary?

You might be missing Arles, but otherwise this sounds very good to me. No major comments really!
You could perhaps save 2 days of car rental if you take the train from Marseille airport to Avignon Centre and rent a car once you are ready to leave Avignon. This said, Marseille airport has some low-cost car rental companies which tend to bring prices down vs. other locations in the region, so shop around!

This looks like a lovely itinerary, but you'll be busy. Being retired, we enjoyed largely the same itinerary, but over a month! And there places we had to omit even then. Going in to Marseille and on to Avignon, I'd use the train and wait to pick up your car. Parking inside the walls is pretty difficult. And as mentioned above, I'd add Nimes and/or Arles, but you'd have to delete something to fit one or the other, unless you use your Monday relaxation day. If you can juggle your schedule, the easiest way to reach both is by train from Avignon, which is inexpensive, easy and quick. We took a bus from Avignon to Pont du Gard, and frankly, it was a pain. The car would be useful there, so perhaps picking it up in Avignon the night before Pont du Gard would work better for you. From Nice, we enjoyed Villefranche-sur-Mer, a short train ride away, but there is also plenty to keep you busy in Nice for 2 days. We were there in the late summer, so lavender wasn't an option, but it might be in June. Would seeing the fields interest you?

We will be staying at friends house in Avignon and they live about a 10 minute drive outside of the city walls so that’s why are going to have the car earlier. I figured it would also be handy to have it for when we visit Pont du Gard and Uzes!

We would love to visit Arles and Nimes but I’m not sure if we can fit them in. Maybe next time!

Do you think keeping our luggage in the car while we visit Saint-Remy is a good idea? I’m a little nervous about doing this but we have time to kill before we can check in our hotel at 3pm.

Also, right now we plan to visit Gordes and Roussillon on Saturday but I’m worried that these villages will be too busy.

Should we visit them on Monday instead?

On which side of Avignon do your friends live? It might make sense to leave the luggage at their place while you visit St Rémy, if that's OK with them!
Otherwise, make sure all of your luggage is hidden.

If your rental car lacks a luggage cover (rare, but it happens), I would just head to Gordes, leave the luggage at the hotel, and visit Saint Rémy another day.

The risk is very, very low, but theft happens, unfortunately...

As for Sat vs Mon in Gordes: does not matter, especially since you are staying there anyway. Does not matter much for Roussillon either. Let the weather and your mood guide you!

At Pont du Gard, you used to be able to hike across the top, and see the graffiti left in the walls by the roman workers.
Also, a lovey day trip from Nice is a drive to Saint Paul de Vence.