The video on Saturday showed the two men standing in front of a banner bearing the name of the Islamic Army in Iraq. One man said to the camera: "I would like to tell my family that everything is OK."
In a statement sent to Aljazeera, the group demanded the French government should end a ban on Muslim headscarves for the release of the captives.
The group referred to the headscarves ban as "an aggression and oppression against Islam and personal freedoms in a country alleging to be a country of democracy".
France's law banning Muslim headscarves in state schools
passed its final parliamentary hurdle in March.
The two captives were identified as Christian Chesnot of Radio France Internationale and George Malbrunot of Le Figaro.
"We give France 48 hours, from the time of publishing the statement, to respond and meet our demand," the statement added.
The two newsmen went missing last Friday on their way to Najaf from Baghdad.
The Islamic Army in Iraq killed journalist Enzo Baldoni last week because Italy refused to heed their demand for withdrawal of its troops from Iraq.
The group also earlier said it had kidnapped an Iranian diplomat and showed the man on a video tape aired by Arabic television channels. The group also reportedly killed two Pakistani captives in July.
Dalil Boubakeur, head of the French Council of the Muslim Faith, said he had never thought the headscarf ban could have such an effect outside of France.
"I am dismayed by the gravity of the emergency situation that has developed," he said. "Let us pray to God that the lives of these journalists are saved by any way possible."
Besides the Islamic hijab, the French law prohibits large Christian crosses, Jewish skullcaps and Sikh turbans from state schools.
The main Sunni Muslim religious organisation, meanwhile, has appealed for the release of the two journalists.
"In the name of the Committee of Ulamas we urge the kidnappers to release the two journalists," said Shaikh Abd Al-Satar Abdelzhawad, a member of the committee.
He simultaneously appealed to France to reconsider its decision to ban prominent religious insignia from state schools.
France is home to five million Muslims, the largest Muslim population in Europe.