Driving abroad is very easy and you soon get used to it. If you're nervous practice on a supermarket car park on a Sunday evening when it's closed.
If you really don't want to drive then just look for gites near airports. Most of France is gorgeous so you need to decide what sort of holiday you want - beach, mountains, city, countryside, wine area, historic area, and then use one of the direct booking companies such as vrbo.com to search for suitable properties.
I actually do most of the driving in France as DH isn't confident about translating French road signs. There are a lot of websites giving advice about driving on the left.
If you want a proper beach holiday with reliable weather, head as far south as you can, either to the Med or the west coast, perhaps even further down past La Rochelle. That said, I should think it's quite hard to find a gite right on the beach, as most resorts tend to have apartments.
The area around Le Lavandou on the Med is accessible via Toulon airport from Stansted. Have a look on HomeAway.co.uk for rentals. But don't tell anyone else!!
driving in France is fine (outside Paris, which is scary, even as an experienced London driver). The wrong-side is more than outweighed by the lack of traffic. Driving on to the eurotunnel is dead easy too.
I second going further South for better weather, also my SIL looked for a place on a british site then rang the place direct and saved 50% by going direct, We always stayed near Nice when I was younger and then drove around the local areas. My friends parents live in France and the book flights early to visit and it costs less that £30 for flight pp, then they hire a car there.
I had never driven abroad until 3 years ago - it is a doddle - just keep telling yourself - "kerb on my side" motorways are easy too. We have just returned from between Bordeaux and La Rochelle - brilliant. We were 30 mins from beaches and near to towns too.