I must admit, we've lived in France for 24 years now, and I never cease to delight in some of the wonderful places we've found off the beaten track. It's great if one can take one's time & meander through on the Routes Nationales & departmentales stopping off here & there instead of blasting down the autoroute (FAR more fun in a Morgan that way). I find the Logis de France website an excellent way to find small hotels en route as you can trace your route on the map & there are markers where Logis are located. You can refine your search by setting criteria. As to Italy, I've never been on a driving holiday there, 'tho we have rented a Villa just outside Lucca & driven around Tuscany a fair bit from that base; I'd love to do more. My cousin Patrick drove down to Sicily & back in his MX5 a couple of years ago a had a great time.
To conclude...if you have the time I'd say both. After all, going from the UK you've got to go through France to get to Italy.