"We do not negotiate on these terms, with these groups," Defence Minister Jean-Yves Le Drian said in a radio interview.
"What we do is use all possible means to ensure the release of hostages, be they these or others," he said. "But we do not play this bidding game because that is terrorism."
He spoke a day after a video of the seven members of the family appeared on YouTube with their abductors who claimed to be from the Islamist extremist group Boko Haram and demanded the release of prisoners.
On Monday France's Foreign Minister Laurent Fabius described the release of the video a "shocking" display of the kidnappers' cruelty.
"A video of the French family kidnapped last Tuesday in northern Cameroon has been released by Boko Haram," Fabius said a in a statement. "For all of us, these images are terribly shocking. They display a cruelty without bounds."
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.
Following the release of a video from the abductors French Prime Minister Jean-Marc Ayrault confirmed that Nigerian Islamist group Boko Haram had claimed responsibility for the kidnapping of a French family,
France "now has the information that Boko Haram claims to be holding" the seven French citizens kidnapped last week in Cameroon, Ayrault said after a top-level meeting following the release of the video on YouTube.
Ayrault said the family is "probably held in Nigeria".
"The video tape... is being studied by our (intelligence) services, who are examining precisely the nature of these claims," he said. "French authorities are in close and permanent contact with Nigerian and Cameroonian authorities."
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Threats made to family
In the video one of the abductors speaks in Arabic while addressing Nigerian President Goodluck Jonathan. "If you want us to release these French citizens, quickly release all our women you are detaining," he said.
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 - a father, mother, four children aged 5 to 12, and an uncle - were seized on February 19 while visiting a national park in Cameroon.