I apologise in advance if this subject has been discussed before.
I recently had a meeting with my bank. All my insurances are through my bank, and while i am aware that some will say that may be more expensive, i have found the rates very competitive, and because i have several insurances with them, i appear to get more discount. However, this visit was to insure a motorcycle, that was not insured with them. The rates were checked and i was quoted almost 60 euros less. Now this is where i was given some information that you may find interesting. My bank representative then asked if i used the bike all the year round. I usually only use it very infrequently in the winter months. As a result, i was told to inform them when it was not being used, and the company would change the cover to third party fire and theft, when it was unlikely to be used. Once i decide it will be in regular use again, inform the company and they will revert to fully comprehensive, saving about 50% of the costs, but still allowing me to use it if i want to. They regularly do this for caravan owners, so they do not have to pay full insurance when the caravan is in storage. Presumably, this would also work for those who only live part of the year in France, and leave a vehicle here for when they visit. I hope this information is of some use. 
Stephen, I wonder if this applies also for house being left vacant for a couple of months at a time.?Thanks for the vehicle info. Exactly what I needed.
For cars, most insurers offer limited kilometrage policies which can save quite a bit if you don’t use the car much. The terms vary - MMA used to give me money back the unused kilometres, Allianz only let you carry them forward to the next year.
MMA give you the choice between a refund for km not used or carrying them over.
Stephen, in a blatant advert for your bank, can you name it?
My bank is Credit Agricole. All the insurances are with Pacifica via the bank. I’ve been with them ever since i have lived in France, and they have been excellent, including helping with subjects which have nothing to do with the bank. As with any bank, services may vary branch to branch, but i have no complaints, and the two bank representatives assigned to me, have both been very helpful.