I don't think you would be on the hook with his insurers should you be involved in a 3rd party claim.

(as long as you could reasonably claim that you did not know he had no license - only that he had a policy which you had seen).

But - if you had an accident in that car, that the insurers paid out on (and that could be hundreds of thousands/millions in extreme cases of personal injury) - the insurers WILL payout on the policy, but will seek to recover those costs from the policy holder (your FiL) - that will bankrupt him (might bankrupt him with a much lesser claim).

As has been mentioned - investigate a policy where you are the principle driver, but otherwise - have that hard talk and suggest he sells the car and takes taxis from now on.