The more than three-minute video shows the family, including four children, held in an undisclosed location, surrounded by at least three of the abductors from the Nigerian group whose faces are hidden.
A source close to the family confirmed their identities to AFP. It was not clear when the video was made.
“If you want us to release these French citizens, quickly release all our women you are detaining,” one of the abductors says in Arabic in the video while addressing Nigerian President Goodluck Jonathan.
He calls on Cameroon to release “our brothers” and warns the group will kill its hostages if its demands are not met.
At the start of the video, the father Tanguy Moulin-Fournier reads a statement from a piece of paper, his four children in front of him, his wife and brother beside him.
The family, with children aged 5 to 12, were kidnapped on February 19 in Cameroon.
Cameroon authorities said the victims, who were visiting a national park at the time, were taken over the border into Nigeria’s restive northeast after being abducted.