A semi-presidential republic, or dual executive republic, is a republic in which a president exists alongside a prime minister and a cabinet, with the latter two being responsible to the legislature of the state. In France, for example, in the case of cohabitation, the president oversees foreign policy and defense policy (these are generally called les prérogatives présidentielles, presidential prerogatives) and the prime minister is in charge of domestic policy and economic policy. In this case, the division of responsibilities between the prime minister and the president is not explicitly stated in the constitution but has evolved as a political convention based on the constitutional principle that the prime minister is appointed (with the subsequent approval of a parliament majority) and dismissed by the president.

Source: Wikipedia