However, he ruled out suspending diplomatic relations with Iran over the crisis.
"We call on the Iranians to free the sailors as quickly as possible and without any concessions," Douste-Blazy told RTL radio. "We must put very strong pressure on the Iranians," he said, adding, "I think we must avoid confrontation and escalation."
The French Foreign Ministry summoned the Iranian ambassador to France on Thursday.
"Today, there is no freeze" in relations, Douste-Blazy said.
His remarks came a day after the U.N. Security Council agreed on a statement expressing "grave concern" at Iran's capture of the British sailors and calling for an early resolution of the problem including their release.
The British government says the Royal Navy crew was seized March 23 after searching a civilian ship in Iraqi waters near the mouth of the Shatt al-Arab waterway, under a mandate from the Security Council. Tehran says the British vessels were inside Iranian territorial waters.