The members of the family -- a couple, their children aged five, eight, 10 and 12 and an uncle -- were abducted while on holiday in the West African nation of Cameroon on Tuesday by six armed suspected Islamists on three motorbikes.
Cameroonian officials said they were taken across the border into Nigeria, though Nigerian military spokesmen would not confirm that information.
One Nigerian security official however said on condition of anonymity that they were searching near the porous border with Cameroon in the country's northeast. The region is on the edge of the Sahara, where insurgents and criminal gangs have long operated.
"We are fully cooperating with Nigerian and Cameroonian authorities to find the location where our citizens are being held," French President Francois Hollande said in Paris.
He said the priority was to "first of all identify the exact place where (they) are being held, probably in two groups".
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 with them at the time and was kidnapped as well. The three adults are all around 40 years old.
The family moved to Yaounde, Cameroon's capital, in autumn 2011 when the father got a job there overseeing the construction of a liquid natural gas plant.
"It's difficult because these are good people," said one of the guards at their home in Yaounde. "We didn't have an employer-employee relationship, they were family," he added.
The Nigerian security official said "intelligence reports have shown that the abductors may be holding their victims ... around the Dikwa area," referring to a town in northeast Nigeria.
"But I must tell you we haven't got the exact location."
Hopes had been raised when a Cameroonian military source said earlier Thursday the family had been found safe and well in Nigeria, abandoned in a house in Dikwa, about 100 kilometres (60 miles) from the border with Cameroon.
France's Veteran Affairs Minister Kader Arif confirmed that claim but later said he had merely passed on a media report. Cameroon's Communications Minister Issa Tchiroma Bakary bluntly stated that it was "a wild rumour".
-- An 'odious act' --
Hollande has condemned the seizure as an "odious" act, saying: "This is the first time that children have been taken hostage in this manner."
The French foreign ministry has urged citizens in the far north of Cameroon to leave the area as quickly as possible and advised against travel to areas bordering Nigeria until further notice.
It could not say how many French citizens are believed to be in the north but 6,200 in total are registered as living in Cameroon.
Foreign Minister Laurent Fabius said France would not give in to "terrorists", an apparent warning that a ransom would not be considered.
The defence ministry said a team of French gendarmes had arrived in Cameroon on Tuesday to help with the probe, adding that they were being "protected by French soldiers".
French Defence Minister Jean-Yves Le Drian pointed the finger at Nigeria's Boko Haram extremist group but said it was not clear whether the kidnapping was linked to France's offensive against Islamist rebels in Mali.
"These are groups that claim the same fundamentalism, who use the same methods, whether it's in Mali, Somalia or Nigeria," he said.
Nigerian officials declined to comment on Boko Haram's alleged involvement.
While French officials have named Boko Haram as the likely culprits, a splinter faction of the group known as Ansaru, which has risen in prominence in recent weeks, appears have targeted Western hostages.
Ansaru claimed the December kidnapping of a French national in northern Nigeria and the abduction of seven foreigners from a construction site in Bauchi state at the weekend.
In statements, Ansaru has protested against France's efforts against Islamist rebels in Mali and warned of further attacks.