Islamist militant group Boko Haram has claimed that it is holding a French family of seven captured in Cameroon last week, France's Prime Minister Jean-Marc Ayrault said on Monday.
The video, which appears to show the family, including four children, was posted on YouTube on Monday.
"(We) have received information that the group Boko Haram is claiming to be holding the French family," Ayrault told reporters, adding that French experts were examining the YouTube video to determine whether it was authentic.
"We have been taken by Jama'atu Ahlis Sunna Lidda'awati wal-Jihad," one of the male hostages said in the video, referring to the name in Arabic of Nigeria's Boko Haram militants. "They want the liberation of their brothers in Cameroon and their women imprisoned in Nigeria."
The kidnapping on Tuesday of the seven French nationals in Cameroon's far north, near the border with Nigeria, highlighted the risk to French citizens in Africa since Paris sent troops into Mali to oust Islamists there.
"The president of France has launched a war on Islam," said one of the apparent kidnappers, warning that the hostages would be killed if their demands were not met.
Cameroon Communication Minister Issa Tchiroma Bakary said he could not comment because his government was not aware of the video.
The governor of Cameroon's Far North Region, Augustine Fonka Awa, said he was not aware of any Boko Haram members being held in the country.