Hello and welcome
You can only be in the social security system of one country. So yes, if he is in the NHS then he can’t be in the french health system except as a seconded worker. For example if his UK employer has sent him to France. If that’s the case then he can get a “worker’s S1” which allows him to join the french health service without paying cotisations.
Otherwise you can be asked to provide a letter from the UK which says you aren’t entitled to NHS care before they will let you join the french health service.
In general once people are resident in france and join the health service they get a CEAM card which covers them for health when travelling in other european counties. So really that is not an issue.
You say he has a 1 year residency card. Does that mean he is not european? As that could also be complicating matters as the rules are different for non-europeans. But if he is resident here then you are aware there is a limit to how much time he can spend in the UK?
The E104 form is probably trying to establish his social security history and eligibility for benefits as he is presumably or working age but has no employment here?