There is no reason for your long-stay visa to automatically become invalid.
France has none of the “duration of status” or “grace period” business that you find in the US for example. The way the system works is that you typically get a one-year visa or a first carte de séjour and after that you must apply for a new carte de séjour every year (for scientists or “highly qualified workers” it can be valid for more than one year) until you qualify a carte de résident. That's when you can be forced to leave.
Every time you apply for a renewal, the authorities evaluate your circumstances. For example, a slew of students get a denial (and also an obligation de quitter le territoire français) in December (that's September plus some processing time) because they failed at their exams or completed their studies and do not qualify anymore. Having left your job, and unless you qualify under some other provision, your application for a carte de séjour would also be denied.
The authorities can also invalidate a carte de séjour before the end of its regular validity period and I guess it's the same for a long-stay visa but it would take some official decision. In practice you would receive a letter informing you of the decision. I am not sure whether they actually do that as a matter of course merely because you left your job (never heard of it) but it would probably take longer than 30 days anyway.
Your right to circulate in the Schengen area in turns depend on your having a valid French visa or residence permit. Until France decides to invalidate said visa, other Schengen states are not supposed to evaluate themselves whether you qualify for it.
Incidentally, note that if you lost your job instead of having left voluntarily, the carte de séjour cannot be cancelled and you would be entitled to an extra year in any case.