Being properly insured for WWOOFing activities is part of your commitments when you join the organization. It is your responsibility to check with your insurance the guarantees and exclusions of your policy. Your WWOOF France membership does not include insurance.
If you live in France
You probably already have a liability insurance. This insurance covers damage or injury to a third party during your WWOOFing activities because WWOOFing is defined as an unpaid activity, just like volunteering or agricultural mutual support. We know that MATMUT, MMA, AXA, MAIF offer liability insurance.
If you come from Europe or elsewhere
We recommend that you take a travel insurance. If you are looking for adequate insurance as part of your WWOOFing experience, you can have a look at WorldNomads that can cover you during your volunteering. They offer many plans, but note that with the basic one, activities will have to remain on land (i.e. without using motorized vehicles).
On their side, hosts also have insurance to cover their farms and farm equipment.