As Stella says, he shouldn’t be applying as an economically inactive person if in fact he is economically active, ie working for a living.
A person who lives in one EU country and works in another is termed a “cross border worker” or a “frontalier” and EU rules make special provision for their healthcare. You will find all the details from google but here is a place to start:
Cross border workers belong to the social security system of the country where they work and pay income tax and social security contributions, and that country also covers their healthcare in the country where they live. But you do have to inform the authorities in the country where you work that you live abroad, and obtain the necessary forms.
Whether this arrangement will continue after Brexit or not, is anyone’s guess.
He needs to contact HMRC and explain the situation to them. He may be told to use his UK issued EHIC card for medical treatment in France, or he may be sent a form by the UK and told to take it to CPAM and get a carte vitale, sometimes people seem to be told one thing and sometimes the other, I have no idea what the deciding factors are. Either way he can’t apply directly for a carte vitale because France is not responsible for his healthcare if he works in the UK. What CPAM needs in his case is confirmation from the UK that any healthcare costs he incurs in France, will be refunded to CPAM by the UK.
Hope this helps.
Odd that he has managed to obtain a residency card without first having to clarify his status in France and produce the appropriate paperwork! I wonder what status the Préfecture thought he had when they issued the tds.