Appointment of the prime minister of France requires no approval by the parliament either, but the parliament may force the resignation of the government. In these systems, it is possible for the president and the prime minister to be from different political parties if the legislature is controlled by a party different from that of the president. When it arises, such a state of affairs is usually referred to as (political) cohabitation.
What is the term for a situation in which the president and prime minister come from different political parties?
cohabitation