The video that France's foreign minister called "terribly shocking" represented the first images of the family to emerge since their abduction in Cameroon on February 19.
The kidnappers, claiming to be from the Nigerian group Boko Haram, say they carried out the abduction in part due to France's "war against Islam," apparently a reference to French military action in Mali.
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 whose faces are hidden. 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, addressing Nigerian President Goodluck Jonathan.
He calls on Cameroon to release "our brothers".
At the start of the video, the father of the family reads a statement from a piece of paper, his four children in front of him, his wife and brother beside him.
Two of the abductors hold weapons and ammunition, while a banner with two rifles hangs behind them.
The family, with children aged 5 to 12, were kidnapped in the West African nation while visiting a national park.
Cameroon authorities said the family was taken over the border into Nigeria's restive northeast.
Despite claims in the video, it was not immediately clear if the abductors were indeed from Boko Haram, which has carried out a violent insurgency for years in northern and central Nigeria but has never before claimed a kidnapping.
Most previous Boko Haram videos have featured suspected leader Abubakar Shekau speaking in the Hausa language common throughout Nigeria's north.
A splinter faction of the group known as Ansaru, which has risen in prominence in recent weeks, appears to have focused specifically on taking foreign hostages.
Ansaru claimed the December kidnapping of a French national in northern Nigeria and the recent abduction of seven foreigners from a construction site in Bauchi state.
In statements, Ansaru has protested about France's efforts against Islamist rebels in Mali among other issues.
Analysts have said a criminal group may be behind the abduction of the family with the intent of selling the hostages or collecting ransom.
France's government has previously blamed Boko Haram and maintained that position on Monday.
"A video of the French family kidnapped last Tuesday in northern Cameroon has been released by Boko Haram," Foreign Minister Laurent Fabius said in a statement.
"For all of us, these images are terribly shocking. They display a cruelty without bounds. We are proceeding with the checks required in these circumstances. All state resources are mobilised to free our compatriots."
On Thursday, French President Francois Hollande said that the family was probably being held in two groups. While all seven were together in the video, it was not clear how recent the footage was.
The family, who were based in Cameroon, were visiting the Waza National Park when they were kidnapped. They have been identified as Tanguy Moulin-Fournier and his wife Albane, as well as their four sons, Eloi, Andeol, Mael and Clarence.
Tanguy's brother Cyril Moulin-Fournier was on vacation and with them at the time. The three adults are all around 40 years old.
The family, with the exception of the uncle, moved to Yaounde, Cameroon's capital, in autumn 2011 when the father began a job there overseeing the construction of a liquid natural gas plant. The uncle lives in Barcelona, Spain.
Nigeria is Africa's most populous nation and largest oil producer, roughly divided between a mainly Muslim north and predominately Christian south.
Boko Haram has called for the creation of an Islamic state in the country, where corruption is deeply rooted and most of the population lives on less than $2 per day despite its oil reserves.