You are right about travel insurance, but it is not really critical just travelling through France as far as i am concerned. Life is always a risk, but this one is not difficult to rationalise. There will soon be an end to UK quarantine for Europeans (watch this space) an FO advice will follow that, so will be nice to get ahead of the crowds.
On vehicle insurance, I doubt it is correct that you would not be covered. If you ring an insurance co. to ask the question, doubtless at the present time, they will just say you are not covered. But it is the contract that matters and unless anyone can point to a specific clause which states that FO advice invalidates your insurance, then it is speculation to suggest there is no cover.