If you're going to be working in France, you'll be covered automatically by the national insurance (Sécu Social) and most likely by an employer-provided mutuelle. It isn't a bad idea to get yourself a travel insurance for the first month or two until you get settled in and started up with work (basically to protect you in case of an accident or serious illness during this time).

If you're not going to be working, you would have had to provide evidence of insurance as part of your visa application process (and that insurance IS expensive).

The health care system in France is a reimbursement system - you pay for your doctor's appointments and most out-patient treatments, then you are reimbursed by the system. The sécu reimburses about 70%, with the mutuelle picking up the rest. (There are some exceptions, but that's the general pattern.)

You pay for the insurance via payroll deduction. The sécu portion is based on a percentage of your salary and covers your whole family, while the mutuelle is normally paid for on a per-person basis, with one monthly fee for each adult covered, and a lower fee (usually about half) for each child covered.

Takes a little getting used to, but basically the system works pretty well.
Cheers,
Bev