Loosely speaking the "Sécurité sociale" is an obligatory health insurance in France, see the right definitions here :
Notice that the state usually does not cover the entire health expenses, but only a percentage of them (around 70%) the remaining expenses are however quite high and they are up to you. For instance the cost of calling an ambulance is about 3000 euro, whose 30% is up to you. Therefore, french people are supposed to have a complementary private health insurance to pay the remaining 30% part.
Notice however that each state has particular agreements with France concerning the health system. So you may not be induced to pay the complementary insurance. The Sécurité sociale is probably necessary.
Before coming in France you should carefully check this point with your embassy.