The newspaper reported that it had obtained the CD-Rom with the recording, believed to have been made earlier this month.
The paper said the recording showed Christian Chesnot and fellow hostage Georges Malbrunot apparently in good spirits, more than three months after their capture by a group calling itself the Islamic Army.
"The behaviour of the Islamic Army has been very good. There is no violence involved," Chesnot was quoted as saying in French-accented Lebanese Arabic.
"We eat three times a day and we get lots of tea and everything is available," he added.
Chesnot said they were being held while "investigations and security problems are finalised" by the Islamic Army.
He also said the security situation in Iraq was affecting their release.
The journalists' kidnapping has
shocked anti-war France
"The situation is very difficult. There is an American siege as well as American patrols and once the investigations and security problems are finalised, we hope to be released," the paper quoted Chesnot as saying.
Earlier this month US marines found the journalists' driver alive in Falluja, 51km west of Baghdad.
The driver, Muhammad al-Jundi, had been kidnapped along with the Frenchmen on 20 August while on their way to the town of Najaf.
The kidnapping of Chesnot, who works for Radio France International, and Malbrunot, who reports for Le Figaro, stunned France, which opposed the US-led war in Iraq.
Paris mobilised a wide front of Arab leaders and Muslim figures to call for their release but thus far to no avail.