Well, that is just the way it is here. And has been for a very long time, which creates a system. In France, any job (bar seasonal) has to have a written contract, quite possibly a simple one, but there must be one.
It may be that, further back, this arises from a difference between Roman law, more written, and Anglo-Saxon law, which relies more on common law. Plus, as I suggested, America has a distinct subset of values on these matters -- which, btw, though I "get" them, I find disingenuous in their assumption of good faith on all sides, of equality in the contractual relationship, and -- especially -- the absence of a power struggle or a balance of power between employer and employee. The right to walk away, excuse me, is piffling compared to an employer's rights and powers. It may be a useful threat in some circumstances, but, most of the time, the firing sanction is a much heavier tool. You're assuming bosses are not present-day Caligulas? Well, maybe they're not in California, (?), but there's a fair amount of anti-employee feeling among French bosses (deeply-seated, going back a good way) that justifies, in my view, the reluctance of young people to see their early job experience exposed to arbitrary employer decisions.
How would this result in lowering the cost of labour? By creating conditions of fragility and precarity for employees in which they will accept less good terms in order to be sure of holding down the job. A boss who can fire at will is a boss who can fix wages and conditions to his advantage unless the job market is tight which is not the case here.
(BTW, the State doesn't force any employer to keep an unwanted employee, that's not the way things are structured. There are contractual relations, there are conventions, there is jurisprudence, that need to be respected, and that is the case anywhere, including the US. An employer can fire an employee if he can show reasonable cause.)
Of course there is a contract. A private one.
What I meant is why -- other than for reasons of minimum wahe, health & welfare -- should it be a STATE-created contract.
Why on Earth is the French Government telling employers what to do with their "Premieres Embauches"?
It's not telling the employer what to do. It's allowing the employer to do things that were not previously accepted, by law, by the jurisprudence. It's saying: from now on, if you hire someone under 26, you're free to fire them at will over a two-year period. This kind of regulation is requested by the bosses' unions. (Though they're backing off from this one now, because it's become a hot potato).
It's not an easy thing to explain without it looking like I'm (me or another) being defensive about a system that isn't necessarily all good (though I must say that Americans can be very aggressive/out-of-hand dismissive about this subject, and that kindles defensive responses). My point, as someone who came from another country with an Anglo-Saxon common law basis, and who had trouble at first understanding what was going on here, is that other ways of doing things exist, and there isn't necessarily a right and a wrong about it.
And don't let me get started about whether it has been demonstrated that the American way of handling contractual relations between employer and employee has been productive of good, equitable results across society. (No, the French way hasn't either, but it does provide lower-level employees with more security, and develops a minimum net of solidarity).