"What we want to promote is an accord between the EU and the UK… This cannot be simply an agreement on readmissions," Gerald Darmanin told a news conference.
He added that France would seek a "balanced" agreement regulating joint response to illegal migration, something that was left out of the Brexit negotiations.
French Prime Minister Jean Castex will write on Tuesday to his UK counterpart, Boris Johnson, to share his vision of the proposed agreement, Darmanin told reporters.
French President Emmanuel Macron called an EU emergency ministerial meeting last week after at least 27 migrants drowned when trying to reach the British coast in a boat. Darmanin said five suspected smugglers had been arrested.