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 on Thursday. 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 on Thursday that 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".
France has said it suspects Nigerian Islamist group Boko Haram was behind the abduction.
Earlier in the week French Foreign Minister Laurent Fabius said France would not give in to terrorists. Seeming to exclude the possibility of paying a ransom, Fabius told the National Assembly: "We must do the maximum [to free the hostages] but nothing would be worse than yielding. We will not yield to terrorist groups."