from Normandy to Marseille, what is the best transportation?

There are non-stop flights from Caen to Marseille on Mondays in August. Check Skyscanner for your dates to see rates.

Nancy : should it be better to drive back to Paris then take a train or fly to Marseille?

From Rouen you could take a train to Lille and then from Lille go to Marseille

Nancy : should it be better to drive back to Paris then take a train or fly to Marseille?

Not sure what you mean by better. It's a 3+ hr drive from Caen back to Paris to drop your rental car, then either train (3-1/2) to Marseille, or flight which would also take a good amount of time. Not to mention the increased cost of road tolls. Why not just arrange to return rental car at Caen airport and fly direct to Marseille and plan to pick up rental car at Marseille airport? Seems easier and may be less expensive and take less time - all of which would make it better for me.

Will you not be near Caen when you end your stay in Normandy? If not, that might change the advice.

This train connection runs every day in August except the 18th and 19th and has the benefit of not going through Paris:

Caen - dep 07:42, IC 3334, Direction: Paris St Lazare

Mantes La Jolie - arr 09:22

Transfer time 9 min.

Mantes La Jolie - dep 09:31, TGV 5316/5317, Direction: Marseille-St-Charles, Subject to compulsory reservation

Marseille-St-Charles - arr 14:21

There are many definitions of "best" but I'm not a fan of flying if the train ride is only five or six hours. You see the countryside and are free to move about. You don't mention the ages of the others in your family but my boys managed long train rides at ages 8 and 11 - bring books, maybe a new travel game, etc. You'll have to research the costs of both methods, sometimes that makes the decision easier.