He said no. Got fired.
Edit - you say you're willing to quit if they don't agree, so I guess you're up for this possibility. More power to you!
But regardless, outside of rare exceptional circumstances (sometimes there's a deadline and shit's gotta get done), I'd recommend anyone to tell their employer to pound sand if they ask for more work from you than you agreed to.
In the US, the vast majority of these positions are salaried. You get $X/year to perform the duties you're expected to. Because we don't have unions and 99.9% of people are not expert negotiators, "the duties you're expected to" are never actually defined. That means your employer is incentivized to stack as many duties on as they can, until they approach your breaking point. So long as they don't break you, it's free work for them. Employers regularly abuse inexperienced people and desperate people, who don't have the confidence or financial wiggle room to say "no." I applaud those who normalize saying "no," and encourage forming unions so there's a group of experts in the room whose job it is to fight back against this kind of abuse.
If you are on call then you get paid x% more during that tile and it cannot be more than y hours per month (I do not remember the values). You also have to have at least 11 hours of rest between the days.
The duties are not clearly defined either (despite continuous ideas on how to measure them, which consistently fail year after year) which is a good thing: it is not easy to have this as a reason to fire you (you have to have a good reason to fire in France).
We value work/personal life proportions a lot, but we also are very serious when it comes to work. It is only from the outside that it looks like we are constantly on vacation or having lunch (this is true for some parts of the workforce, to the point of becoming a stereotype).
This is required by law? Yeah we definitely don't have something like that in the US (except for life-endangering roles like doctors, truckers, airplane pilots, etc). It's up to each individual to negotiate their acceptable amount of on-call time and compensation.
(Just to be clear, "being on-call" doesn't mean you are actively working, just that you agree to be responsive if someone reaches out to you about a problem. That could take 15 minutes or 4 hours to resolve, but if no one calls then you are not actually working during the on-call time.)
My guess is that they wanted a reason to fire your guy anyway, and he gave them one.