Worried about car hire in France

When hiring a car abroad, as long as your licence is valid and not suspended, you would be able to hire a car - at least most of the time with most car rental suppliers.
As each car rental company has its own set of rules, you should ask if points on your licence matters or not. However as mentioned above, abroad in most countries it is OK.

The situation changes though when try to hire in the UK... most of the rental companies will not accept if you have points on the licence. It also matters what are the points for. So be aware of that if ever need to rent a car home.

Extra insurance is not required but if you have it it gives you peace of mind.
Now depending on your budget, you can choose a third party insurance which is fairly cheap (I recommend to get extended cover which includes wheels, glass underside and roof), or you can get zero excess cover (Smart cover or SCDW from the supplier) which is much more expensive, but in case of damage or theft you have no liability at all.

I hope this helps