That’s because it’s convenient to get there by public transport
That was my Point, people who drive right now don't use Public Transport because it isn't convenient for them.
Instead of burning funds to make it free for People who are perfectly capable of paying 300€/Month for their Car, you should use it to expand the Networks (New Train/Tram/Bus Routes) and augment their quality (Longer Operating hours/ Higher Service Frequency) and let them participate a Bit in the Costs, so you can improve the Network even further. (If they we're able to pay 300€/Month for their Car, they can certainly pay 50-100€ for a monthly subscription too)
Taking the TGV from Strasbourg to Montpellier still gets you a Lot of painful slow legs inbetween. And they aren't very comfortable for long journeys.
Also the French Global Price system with Random timetables and mandatory Reservations Sucks badly