A video posted on YouTube Monday appears to show the seven French citizens who were kidnapped in Cameroon last week.
It shows the seven hostages - three adults and four children - sitting in a small tent, surrounded by gunmen.
The French Foreign Ministry said it was trying to verify the authenticity of the video. Foreign Minister Laurent Fabius said the images were "terribly shocking and show cruelty without limits."
In the 3:25 minute recording, a male hostage says that they were abducted by Jama'atu Ahlis Sunnah Ladda'awatih wal-Jihad, better known as Nigeria's Islamist insurgent group Boko Haram.
The hostage reads from a paper that the hostage-takers have demanded the release of Islamist militants jailed in Nigeria and Cameroon.
The seven-member Moulin-Fournier family were kidnapped from the far north of Cameroon, near a national park close to the Nigerian border, on February 19.
The French Foreign Ministry last week denied earlier media reports that they had been released. Citing Cameroonian military sources, French media had reported last week that the expat family had been found unharmed in a house in northern Nigeria.
Tanguy Moulin-Fournier, an employee of the GDF Suez energy company based in Cameroon's capital Yaounde, was abducted with his wife and children during a visit to a wildlife park in the far north of Cameroon. Another male adult, believed to be a relative or friend, was also in the group.
It was not clear where the hostages were being held.
French Prime Minister Jean-Marc Ayrault has said that Boko Haram has claimed responsibility for the kidnapping