Please do not assume that the storage owners in France are insured for the building in which the caravan is parked.
We always advise you to insure your caravan against theft, fire and damage. In some cases, the storage locations in France are insured against fire and theft damage. However, this does not mean that your caravan / vehicle is insured with it. It is therefore wise to ensure the caravan but this decision is up to you.
A company in the UK which can provide insurance for storage in France is Shield Total Insurance.
If you decide to park your caravan uninsured in storage, keep in mind that damage caused by your caravan to third-party caravans and property of the storage owner falls under your own responsibility.