"The kidnappers have crossed the Nigerian border with their hostages," junior minister Joseph Dion Ngute said in a statement late on Tuesday.
He added that security in the Dabanga area, 10 km (six miles) from the Nigerian border, had been reinforced and "urgent measures" put in place to find the hostages.
It is the first case of foreigners being seized in the mostly Muslim north of Cameroon, a former French colony.
Speaking on French television on Wednesday, French Defence Minister Jean-Yves Le Drian said all the evidence pointed to Nigerian Islamist group Boko Haram, but there did not appear to be a direct link with France's intervention in Mali.
"We believe it's the Boko Haram group that carried out the kidnapping, but we don't know for sure. Unfortunately, terror breeds terror," Le Drian told France 2 television.
"Now this group ... are taking children."
Boko Haram are a major threat to stability in Nigeria, Africa's top oil-producing state. Western governments worry they could link up with other Islamist groups in the region.
France intervened in Mali last month after Islamist rebels seized control of the north of the country and pushed south towards the capital Bamako.
"It's these groups that are calling for the same fundamentalism, whether it's in Mali or in Somalia or in Nigeria. And it's these groups that threaten our security," Le Drian said.
French President Francois Hollande said the kidnappings would not stop France from pursuing its operation in Mali.
Le Drian's predecessor, defence minister during France's 2011 intervention in Libya, said the kidnapping could be a turning point.
"If it's proven that it's the Boko Haram terrorist group, that's a significant event for Africa because that means this group is intervening outside its borders, in a calm, independent country," former defence minister Gerard Longuet told BFM-TV.
"It's a real international political problem."
The kidnapping of the family brings the number of French hostages held hostage in isolated regions of west and north Africa to 15.
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