The hostage video was broadcast Friday by Sahara Media in Mauritania, Radio France Internationale reported. Sahara Media said it was made in the last months of French President Nicolas Sarkozy's term. He left office May 15.
The men were kidnapped in Mali and Niger, allegedly by al-Qaida in the Islamic Maghreb, the al-Qaida affiliate in the region. They were shown in the video surrounded by armed men.
Phillipe Verdon, a geologist abducted with a colleague in Mali, said on the tape that AQIM is "available to negotiate." He appealed for help winning their release.
Verdon said he had been unable to get medication for an unspecified condition for three months.
AQIM is holding another group of French hostages, four men abducted in 2010 from a uranium mine in Niger. The al-Qaida group has said they will be released once France pulls out of Afghanistan.
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]
Reindeer recovered after escaping from Santa during lighting ceremony