You are the only person who can determine which you would prefer.
Questions...do you believe you would be comfortable driving in France? Many of the roads are quite narrow but those are often the most scenic. Do you believe you could follow the road rules? You can drive the circle of the roundabouts more than once. Trust me...my husband and I have done that many times?
How much time do you want to spend in each area? Do you know the train schedules for the places you want to visit on the day trips? Would using a car make it easier or do the train schedules work to allow you to see what you want? How much time do you want to spend in a car versus being on a train?
Are you willing to pay the tolls if you drive on the main roads? Do you plan to go from Lyon to Provence and then to Strasbourg and Annecy? Have you looked at the mileage for each?
We have spent a lot of time in Provence. Provence is a large area. What part of Provence do you want to visit? For example, if you want to be in the Luberon, a car would be best to allow you to more towns. The trains run to the larger cities such as Avignon but to go to the Luberon hill towns, you would want a car. I do not know anything about possible buses.
Many posters on this website swear by trains. My husband and I have used trains twice but most of the time, we have rented cars. We like to go to the off beat, back roads places. As I said, you have to decide what you want to do, what you want to see and if you are willing to do the driving. France is a country about the size of Texas so you could be doing a lot of driving.
Regardless, have lots of fun! I always envy those of you who are getting to go to France in the very near future!
Bev