Yes, this is called rachat de franchise. Most car hire firms offer basic insurance, including an excess to be paid in the case of a claim due to an accident, which can be high.
They may also offer additional cover so there is no excess but this may not cover all kinds of damage and could be costly.
So an independent rachat de franchise policy is an option, whether by the day or year, with forms such as SereniTrip and Euro Assistance.
Some credit cards also have this insurance cover included in the service, so it is worth checking with your card provider.
Reader's query answered by Hugh MacDonald
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