The Constitution
The government follows the Constitution of the Fifth Republic. It was put into action on 4th October 1958. It is based on the principles set by General de Gaulle during his famous speech on 16th June 1946.
The Prime Minister
France has a Prime Minister who is the Head of Government. He directs the actions of the government. He cannot force the other ministers to do what they do not want to, but he may ask the President of the Republic, who is currently Emmanuel Macron, to dismiss them. He can also propose to the President of the Republic to appoint new people as ministers. He's responsible for defending the country.
The Council of Ministers
The Council of Ministers is when all the ministers gather to discuss important issues. They meet every week with the Prime Minister and the President of the Republic. They normally meet on Wednesdays at the Elysée Palace. The Prime Minister will propose ideas and the President will either approve or disapprove of them.