The hostages -- a man, his wife, his brother and the couple's four children -- are shown in good health sitting in a tent made from prayer mats and in front of a black al-Qaida-style banner, The New York Times reported Tuesday. The father was identified as Tanguy Moulin-Fournier.
A masked gunman reads a statement in Arabic in the video released Monday, demanding the release of "brothers" and "sisters" or they will "slaughter those we took."
The speaker warns Nigerian President Goodluck Jonathan that the group plans to establish an Islamic state in Nigeria.
"We say to you: If you want us to leave those French people, leave all of our women whom you imprisoned by your hands quickly, because we know that all ways of disbelief are the same, and all of you are equally in war with us," the gunman adds.
Moulin-Fournier read a statement in French saying the family was "arrested" by militant Islamic group Boko Haram.
The Nigerian group denied involvement in the kidnapping at a news conference Sunday.
Boko Haram hasn't previously been known to kidnap Westerners, the Times reported.