When they do need to visit family in the more rural areas, they either take the train, or use a carpooling service (the most popular one is blablacar.com, which has been taking off like crazy in the recent years. The vast majority of French people I talk to when I go back home have heard of it- one of the few innovative French startups).
In France, I spent a year and half and about 1500 euros in driving lessons related stuff and didn't get my license. When I first moved to the US (southern state), it cost me something like 30 bucks and 30 minutes of my time. The test consisted of driving around the block, and parking the car (only snag: the inspector by my side, a rather overweight lady, told me that I'd lose points the further away I parked from the DMV's front door. I thought she was joking, but she wasn't).
The conservative French people say that more expensive, stricter, longer times for obtaining a driver license leads to safer roads; but if you compare US driving fatalities to French ones, there's not much of a difference- and people in the US drive way more than they do in France.
Like many other aspects of French culture, it's ridiculous how deeply legislated it is, and how the only ones benefitting from it are the ones making the rules. I find certain aspects of the US driving culture a little too much on the other extreme of the spectrum (learner's permit at 14? the driving test being just a drive around the block? the written test being a multiple choice questionnaire with the answers available on YouTube?), but France is worse by far, and it's hurting young professionals (my brother is without a college degree, and when he was unemployed he found that most jobs in rural areas require a car- but getting a license takes forever and is expensive. So that was a few months where he could do little but wait to get his driving license).