A video published on YouTube appears to show seven members of a French family, including four children, abducted by Islamist group Boko Haram in Cameroon.
The footage shows an armed man reading a statement in front of two men, a woman and four children.
Claiming to be from the Nigerian militant group Boko Haram, the alleged kidnappers demand the release of prisoners in Cameroon and Nigeria.
The family was snatched last Tuesday by gunmen on motorbikes.
Following the abduction, the French government said it believed the couple, their children aged five, eight, 10 and 12, and an uncle were taken across the border into Nigeria, probably by Boko Haram.
The family lives in the Cameroonian capital, Yaounde, where the father worked for the French gas group Suez. They had been returning from a visit to Waza National Park when they were kidnapped.
On Thursday, France confirmed it had “received information that the group Boko Haram is claiming to be holding the French family”.
“These images are terribly shocking and display cruelty without limits,” French Foreign Minister Laurent Fabius said in a statement.
In the video, one of the male hostages said they had been kidnapped by Jamaatu Ahlis Sunna Liddaawati wal-Jihad – the Arabic name for Boko Haram.
One of the alleged kidnappers warned that France had launched a war on Islam.
Behind him, the alleged family is shown flanked by two armed men in camouflage uniforms.
A source close to the family confirmed their identities to the AFP news agency.
Laurent Fabius said it was still trying to verify the authenticity of the video.
Last week, a French minister wrongly confirmed reports that the family had been found and released in Nigeria.
Meanwhile, French nationals have been urged to leave northern Cameroon “as quickly as possible”.
The French foreign ministry said on its website citizens were “officially advised not to go to the far north of Cameroon (the shores of Lake Chad in the South Maroua), and the border with Nigeria, until further notice”.
Boko Haram has staged many attacks across northern Nigeria in recent years, targeting churches, government buildings and the security forces.
Another Islamist group – Ansaru – is also active in the region.
Last Sunday, Ansaru claimed the abduction of seven foreign workers in Nigeria.
Italian, British, Greek and Lebanese workers are thought to be among those held after an attack on a construction project in Bauchi state.
Ansaru also says it is holding a French national, Francis Colump, who was seized in the northern state of Katsina.