Seven French tourists from one family, including four children, were kidnapped in Cameroon on Tuesday by suspected Islamist militants.
French President Francois Hollande said he was informed that they were seized by a Nigerian "terrorist group that we know well", without naming it.
"What is most probable is they will be taken to Nigeria," he told reporters on a visit to Athens, adding that France was doing everything possible to prevent that outcome.
A source close to the French embassy in Yaounde said a group of men, apparently on motorbikes, had captured the seven tourists in the northern village of Dabanga near the Nigeria border after they had visited the Waza nature park.
Asked whether the kidnap could be a reprisal for France's military offensive against Al-Qaeda linked groups in northern Mali, Hollande spoke of Nigeria's Islamist Boko Haram group.
"I note in particular the presence of a terrorist group, namely Boko Haram, in that part of Cameroon, and that's worrying enough," he said.
A Cameroonian security source also told AFP: "We have strong suspicions regarding the Islamist sect Boko Haram", which is blamed for killing hundreds of people in an insurgency in northern Nigeria since 2009.
An anonymous source in Waza park said the tourists had visited it on Monday. "They slept in the park's tourist camp where they left this morning," the source said.
A security source in the area told AFP that security forces were hunting for the kidnappers along the border with Nigeria.
It is the first time that Western tourists have been kidnapped on Cameroonian soil but there have been several incidents of hostage-taking off the coast.
Cameroonian authorities have attributed attacks and kidnappings off the Bakassi peninsula neighbouring Nigeria to pirates. The area is believed to be rich in oil and gas.
Some Boko Haram members are believed to have gone to northern Mali to train with Al-Qaeda branch in the Maghreb, but it is not clear if closer ties have developed.
In December, French engineer Francis Collomp was kidnapped in Nigeria in an act claimed by the Nigerian radical Islamist group Ansaru, which is thought to be a Boko Haram splinter group.
On Monday, Ansaru also claimed the kidnapping of seven foreigners in a deadly weekend raid on a construction site in northern Nigeria.
Tuesday's abduction brings the total of French hostages abroad to 15, all in Africa and at least six of whom are being held by Al-Qaeda in the Islamic Maghreb (AQIM).