It is widely recognized that "market failure" prevents efficient risk sharing in natural disaster insurance. As a consequence, many countries adopted institutional frameworks presenting public sector participation, often praised as public-private partnerships. We define risk selection as a situation where private companies pass insurance of high risk agents on to the public "partner", arguing that this is a potentially important issue in such situations. In order to illustrate our concerns we look at the case of France. We build a simple model that incorporates the main features of the system, such as the uniform premium rate in both high and low risk regions and the existence of a state reinsurer. We show that in our model, risk selection is likely to be present at equilibrium and discuss the policy options available. When comparing with the actual situation in France we find that the "stylized facts" of the system correspond to our results. Additionally, the policies implemented by the government correspond to policies characterized to reduce the potential of risk selection.