Mohammed Bechari, vice president of the Muslim French Council, told reporters at a news conference in the Iraqi capital that "we have received proof they are alive and well. We are optimistic and confident they will be released soon."
Bechari did not say what kind of proof the delegation had received.
Bechari publicly appealed to the kidnappers today to release the two men.
"In the name of Islam, in the name of the Arab and Muslim world, we call on the kidnappers to make sure they do not mix up the fights. A journalist's combat mission is to bring us information so that Iraq is not isolated from the world. These two innocent journalists should not be hurt, when France has always been on the side of international law and the respect of dignity," Bechari said.
An extended 48-hour ultimatum from the kidnappers to the French government to rescind the head-scarf ban ended late yesterday.
France has refused to revoke the ban.
The delegation says it is in Iraq to spread the message that French Muslims reject the kidnappers' demands and tactics.
"We tell you that France is not at war with Islam or the Muslims, and that the law about secular education is not a specific law nor a declaration of war against any specific religious community. Secularism is the space that allows us to live all together, religious or not, Muslim or Catholics -- that allows us, above all, not to respond to provocations like this one," Bechari said.
Yesterday, Arab League Secretary-General Amr Musa -- speaking in Beirut -- also appealed for the hostages' release.
"I once again appeal to whoever can help make the release of the two French hostages happen, and we are acting on humanitarian and political motivations," Musa said.
French Foreign Minister Michel Barnier was back in Amman today. He has been traveling between Arab capitals this week, appealing for help in securing the release of the two reporters.
French Defense Minister Michele Alliot-Marie defended France's decision to ban conspicuous religious symbols from public schools in comments today. She said parents can send their children to religious schools if they so choose.
The group that says it is holding the French journalists -- the Islamic Army of Iraq -- is believed to be linked to Sunni militants fighting U.S.-led forces in central Iraq. Last week, the group claimed responsibility for killing another kidnapped journalist, Enzo Baldoni of Italy.
Scores of hostages from dozens of countries have been seized in Iraq in recent months. Many have since been released, but around 25 have now been killed, including 12 Nepalese hostages who were executed earlier this week.
Today, Al-Jazeera television broadcast parts of a video purportedly showing members of a militant group killing three Turks who were being held hostage.
At least another 20 foreigners are still being held, from countries including Bulgaria, Canada, Kenya, India, Turkey, France, Somalia, and Egypt.