The reason I ask is that quite a few of the letting agencies in France offer specialised insurance for rental properties which can cover periods of non rental also.
For insurance, you should call Axa in Nice. They have a team of English girls who offer insurance all over France. My experience with them so far has been very good.
AXA Insurance – Agence Limonier - Nice · -
Call Christina Wingfield, your British insurer on the Riviera for 10 years. Competitive prices for ALL your insurance needs direct from AXA. Home, car (including UK plates), life insurance and health. Claims dealt with in English. Call 04 97 117 117.