The Boko Haram group claims it is holding seven French nationals captured in Cameroon last week.
French prime minister Jean-Marc Ayrault acknowledged on Monday the government has received information that Boko Haram claims to be holding them.
Mr Ayrault said a YouTube video that appears to show the hostages, is being examined to determine whether it is authentic.
The family was kidnapped last Tuesday by gunmen on motorbikes. They had been returning from a visit to Waza National Park.
AFP reports the hostages are Tanguy Moulin-Fournier, his wife, Albane, his brother Cyril and their four children.
In the three minute video, one of the male hostages said they had been kidnapped by Jamaatu Ahlis Sunna Liddaawati wal-Jihad - the Arabic name for Boko Haram.
Behind him, the family is flanked by two armed men in camouflage uniforms.