“We must be very, very firm to win the immediate release of these hostages,” said Royal in a television interview.
Asked about possible sanctions, Royal said there should be “a decision at the European level in that vein, starting with economic (sanctions), then diplomatic.”
US President George W. Bush on Saturday referred to the British detainees as hostages as Britain reaffirmed its desire to resolve the dispute peacefully.
The 15 British navy personnel were seized on March 23 during what Britain insists was a routine anti-smuggling patrol in Iraqi waters under a UN mandate.
Iran however maintains they had strayed into Iranian territorial waters.
Tehran has refused to bow to pressure to release the Britons, who are being held in a secret location and occasionally paraded on state television allegedly confessing and apologising.
France has called for restraint in the row, with Foreign Minister Philippe Douste-Blazy saying that everything must be done to avoid an escalation between Britain, its European partners, and Iran.
EU foreign ministers meeting in Germany on Friday warned in a statement that unspecified “appropriate measures” would be taken unless Iran releases the 15 sailors.
Royal, who is campaigning to become France’s first woman president, said “there should be no weakness” when it comes to Iran and reiterated her view that the Islamic regime should be banned from developing nuclear power, even for civilian use.
“There is no justification for this type of violence and we must be very firm with the Iranian regime,” said Royal in the interview with Canal+ television.
Royal is in close second place in the polls for the April 22 presidential vote, behind rightwinger Nicolas Sarkozy, the candidate of the governing party.
