There has been a surge in clashes in recent days between suspected members of Islamist sect Boko Haram and the military in Nigeria's northeastern town of Maiduguri, near the border with Cameroon.
Security forces and Western diplomats believe it could be an attempt by Boko Haram to draw Nigerian troops into conflict within the city and limit their search and rescue capability.
"There is a massive manhunt ongoing," National Police spokesman Frank Mba told Reuters.
"Security operatives are working around the clock with search and surveillance to solve this."
The French hostages and kidnappers were near a small town called Dikwa at one point on Thursday, a Nigerian military source in Maiduguri said, asking not to be identified.
Dikwa is about 50 miles from Maiduguri and about the same distance to the border with Cameroon, where the three adults and four children were taken hostage on Tuesday.
French gendarmes backed by special forces arrived in northern Cameroon on Wednesday to help locate the family, a local governor and French defence ministry official said.
The abduction was the first case of foreigners being seized in the mostly Muslim north of Cameroon, a former French colony, and highlighted the threat to French interests in West Africa since Paris deployed thousands of troops to Mali to oust al-Qaida-linked Islamists who controlled the country's north.
The region - like others in West and North Africa with porous borders - is considered within the operational sphere of Boko Haram and fellow Nigerian Islamist militants Ansaru.
On Sunday, seven foreigners were snatched from the compound of Lebanese construction company Setraco in northern Nigeria's Bauchi state, and Ansaru took responsibility.
Boko Haram frequently clashes with security forces in its stronghold Maiduguri but witnesses said there has been a surge in attacks in the last three days.
The military in Maiduguri declined to comment.
Many people were killed when suspected members of Boko Haram blew up a customs office, destroyed roadside stalls and fought gunfights with the military on Thursday, three witnesses and a military source said.
"After the explosion the Boko Haram started sporadic shooting with rapid propelled guns leading to the death of many people," a commander in the military Joint Task Force told Reuters, asking not to be named.
Two corpses lay outside a police station on Friday, believed to be those of militants, witness Aminu Hakuri said. Three people were killed on Wednesday when a bomb targeting the security forces exploded in central Maiduguri.
Northern Nigeria is increasingly afflicted by attacks and kidnappings by Islamist militants. Ansaru, which rose to prominence only in recent months, claimed the abduction in December of a French national who is still missing.
Three foreigners were killed in two failed rescue attempts last year after being kidnapped in northern Nigeria. Ansaru, blamed for those abductions, warned this could happen again.