PARIS—President Emmanuel Macron is redrawing the line that separates religion and state, in a battle to force Islamic organizations into the mold of French secularism.

In recent months, his administration has ousted the leadership of a mosque after temporarily closing it and poring over its finances. Another mosque gave up millions in subsidies after the government pressured local officials over the funding. A dozen other mosques have faced orders to close temporarily for safety or fire-code violations.

The government has taken these actions as a precursor to a much broader push to rein in the independence of mosques and other religious organizations across France. Mr. Macron has submitted a bill to Parliament, called the Law Reinforcing Respect of the Principles of the Republic, that would empower the government to permanently close houses of worship and dissolve religious organizations, without court order, if it finds that any of their members are provoking violence or inciting hatred.

In addition, the bill would allow temporary closure of any religious group that spreads ideas that incite hatred or violence. Religious organizations would have to obtain government permits every five years to continue operating, and have their accounts certified annually if they receive foreign funding.