What about the European Health Insurance Card? If you can get one of those, do it. I've got one.
I usually buy travel insurance, especially if I am going to kite buggy on the beach. If you aren't planning anything especially dangerous and the cost is very high, I wouldn't worry if I didn't buy it. France is no more dangerous than the UK.
For all other European holidays we used the EIHC card.
The UK EHIC won't cover everything as it isn't the same as private insurance. Don't think that you will get NHS cover in another country via the UK's EHIC.
When I last looked, for France the UK site says that a French ambulance is billed if the doctor says that the ambulance wasn't needed. The UK won't pay that bill.
In some EEA countries, the relatives have to carry out the basic care while on a ward. The UK won't pay for a nurse. Some EEA countries require a patient contribution and you will pay that, not the UK. Some countries give treatment at a reduced cost, and the UK won't pay that.
Nor will the UK pay to get that holder back to the UK. There are often money raising activities to pay for getting someone back to the UK on an air ambulance as they didn't take out private insurance. That happened to someone in an office I used to work in.
There are warnings on the forums for countries too, like Spain. Taxis drivers like to take tourists to the American hospitals there instead of the Spanish hospitals and they aren't covered and the health bills are massive.
I never leave the UK without full private insurance. I'm not going to risk it with just an EHIC.
Some policies say they will cover what an EHIC won't, which means you have to take the EHIC as well as the private policy.