Upvote:5
In my opinion it would be smarter on your part to subscribe an ad hoc insurance in your home country. I imagine it would be easier to file a claim from the UK with a UK company rather than having to do this over the phone with a French company. To this purpose you should look for European car insurance, which extends the basic insurance cover - the minimum needed to drive legally in Europe - which should be included by default in your preexisting UK instance contract.
A quick search on a comparison website might come in handy here. A random query on Google revealed this company which seems to provide a policy with annual foreign use included.