However following the UK vote to leave the EU (BREXIT) the EHIC card has been replaced with a GHIC Card.
A UK Global Health Insurance Card (GHIC) gives you the right to access state-provided healthcare during a temporary stay in the European Union (EU). If you are British and travelling to France or the EU you will need to have travel insurance with medical cover as the GHIC card will not cover all treatments and healthcare, but it will cover emergency treatment and visits to A&E. Each family member must have their own GHIC. You can apply online and there is no fee. There are companies which claim to assist you with your application for a fee – this is not necessary. You can apply online via the UK NHS website here: https://www.nhs.uk/using-the-nhs/healthcare-abroad/apply-for-a-free-uk-global-health-insurance-card-ghic/
Note: You do not have to apply for a GHIC card if your old EHIC card is still valid.
New EHIC card
Some people are eligible for a new UK-issued EHIC card if they are covered by the Withdrawal Agreement. For instance UK state pensioners living in Europe pre-Brexit. The details are on the website mentioned above.
If you become a resident of France and register with the French national health service – you will be entitled to a European Health Insurance Card which will cover you if you visit other European Economic Area countries including the UK. This also is not an alternative to travel insurance .