Provence is largely rural. You will be able to see more, and further, if you rent a car for part of your stay in Provence. Parking is a minor issue in my view. Trains, buses, and bicycles have their charms--and could also be part of your plans if you like--but will not take you as deep as a car.
With 12 days, consider renting a place in a small town or in the country, with parking included, for a week. Use that time to explore the countryside with a car. If you would like to be car free for part of your trip, spend the balance of your time in a city that is served by rail and bus.
Other considerations: You'll get a better rate, if you rent, if you make reservations before you leave. Also, you can generally return a rental anywhere within France without a special drop-off fee.