International audience The yardstick competition between European health care system is not calling for the french system. Disability-free life expectancy at 65 is, for example, at a better level in few North European countries for a same level of public health expenditures than the french system. As the health french system is original because of its mixed private and public health insurance coverage system, some recent institutional reforms introduced incentives to develop individual preventive care attitudes and a new health insurance market design where private insurers invests in preventive action. In that way, the National Interprofessional Agreement that was established since 2016 between insurance companies and private firms, generated new forms of health insurance contrats that includes a free offer of preventive care. The purpose of the paper is to evaluate the impact of this free health preventive service on the optimal decision between self insurance (vs self protection) and private market demand insurance by policyholders. We demonstrated that the standard properties of insurance model in the line of Ehrlich and Becker (1972) call into question. Our results raised the debate on the optimal design market between the health profile of the insurant and its choice of health coverage.