Herve Gourdel, 55, was kidnapped on Sunday by Jund al-Khilifa, or "Soldiers of the Caliphate," while hiking in a national park that was once a major draw for tourists but became a sanctuary for IS-linked militants.
It follows a call by IS for Muslims to kill Westerners whose nations have joined a campaign to battle the militant group in Iraq and Syria.
The video, entitled "A Message with Blood to the French Government", was posted on jihadist websites.
It begins with a clip of French President Francois Hollande before showing Gourdel on his knees with his hands behind his back, surrounded by four armed militants whose faces were covered.
One of the militants reads a speech in which he denounces the intervention of the "French criminal crusaders" against Muslims in Algeria, Mali and Iraq.
It came a day after Hollande vowed not to give in to the jihadists' 24-hour deadline to end air raids in Iraq.
"As grave as this situation is, we will not give in to any blackmail, any pressure, any ultimatum, no matter how odious, how despicable," he said on the sidelines of an official trip to New York.
France has ruled out joining military operations in Syria, where a US-led coalition began strikes against IS on Tuesday.
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