This thesis deals with the place of private health insurance in the overall health insurance scheme in France, focusing on social inequalities and on solidarity between healthy individuals and sick patients. It particular, it addresses the role of private health insurance on access to health care, mutualization of health expenditure, and welfare. The results of this thesis reveal the key role of private health insurance to access to care postponed over time for financial reasons. However, our results also show that generalizing complementary health insurance in the current health insurance scheme does not allow pursuing equity goals nor increasing welfare. They finally reveal that the mutualization induced by private health insurance appear...