"Mr President, I am still alive, but for how long?" Denis Allex says in the footage, which was apparently released by the Shebab, the Somali guerrilla group that has held him for more than three years.
"That depends upon you," he continues. "For if you do not reach an agreement for my release, then I am afraid that this will be the last message you receive from me. My life depends on you."
The four-minute film, which shows a pale but healthy-looking Allex reading a statement in French in front of a plain maroon curtain, was released by SITE, a US-based private service that monitors extremist websites.
In the video, Allex says he is speaking in July, three years after gunmen stormed his hotel in the Somali capital Mogadishu and seized him, along with a fellow French officer who has since escaped.
It is not clear why the tape took so long to surface as it appears to have been shot to mark Hollande's assumption of the French presidency following his May election victory over then-president Nicolas Sarkozy.
"Mr President, I would like to seize the opportunity of the general political changes and in particular the changes at the head of state level to renew my appeal for help," Allex says in the tape.
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"This time I address it to you, hoping that your handling of my case will be different from that of President Sarkozy and his government," he says, blaming his continued detention on France's stance toward Islam.
French officials have said Allex and his colleague were in Mogadishu to give advice and training to Somali government forces, locked in a fierce fight with the Shebab and other rebel militias.