Hi Sarah. How long have you been in Switzerland? You can keep your foreign plates and driver's licence for up to one year, after that you must change them to local ones.

The car needs to be imported for sure in order to get Swiss number plates. I think if you owned it for more than 6 months in the UK you don't need to pay import tax but you need to doule check on that. You will also need Swiss insurance in order to get the Swiss plates and you need to pay the Swiss road tax and get the sticker to use it on motorways in Switzerland regardless of what plates and insurance it has. I think this voids all other questions.

Also importing a car involves dealing with an experienced intermediary and quite a little bit of paperwork and costs. The car will have to pass the mandatory Swiss inspection and this mey require additional costs depending on the state of the car. If the car is not very high end, you might be better selling it in the UK and buyin one in Switzerland to spare yourself the headache.

I cannot comment on what applies if the car is registered in France but I believe you can have only 1 primary residence and the car and insurance might be tied to that, maybe others can answer that

I hope this helps.

From the French side,

France does not have road tax, but tolls on highways. (paid approx 60eur in tolls yesterday from Cherbourg to Geneva).

You can get French Insurance pretty cheap online, but the car will need French plates. 

all you need to know about importing is here:

http://riviera.angloinfo.com/countries/france/motoregister.asp

You can keep your UK reg in France like Switzerland for 12months, but bear in mind, your insurance at home will most likely only cover you for max 3 months abroad at any one time, be careful with that, especially with some nutty french drivers around...

Honestly, If I were you, and having experience driving all sides of the spectrum, (left hand on left hand, left hand on right hand etc etc), I would just put your motor up for sale in UK and use the cash to buy something down here. Easier driving with the wheel where it should be. And an advantage in FR (not sure about CH) but a CT (MOT) has to be done before every sale, so you'll be sure it'll drive at the very least on a sale. I've bought two cars so far, not had an issue.

Good Luck.