"A growing situation of insecurity is resulting from the intervention undertaken in Mali against the advance of terrorist groups," the advisory from the consulate said.
"In retaliation, Nigerian terrorist groups have issued direct threats against France and French citizens."
The nature of the threats was unclear, and a French official declined to elaborate when contacted by AFP. The statement added that "in these conditions, the risks of attack and especially kidnapping are very serious."
"The area of (extremist) action is the north, but we cannot rule out that it can happen anywhere," a French diplomat said on condition of anonymity.
"That is why we are raising the alert level."
In December, radical Islamist group Ansaru claimed the kidnapping of a French citizen in northern Nigeria, citing France's then push for military intervention in Mali as a justification.
It also warned in the claim that it would carry out further attacks against French interests if the country's stance did not change.
French-led forces on Monday seized Mali's fabled desert city of Timbuktu in a lightning advance north as Islamists fleeing the city torched a building housing priceless ancient manuscripts.
Nearly 8,000 African troops from Chad and the west African bloc ECOWAS are expected to take over the baton from the French troops, but their deployment has been sluggish with 2,700 split between Mali and Niger.
Nigeria is to command the ECOWAS force and contribute 900 troops.
Nigerian Islamist extremist group Boko Haram has long carried out a violent insurgency in northern and central Nigeria. Ansaru has appeared more recently and there is speculation over whether the two are linked.
There has also been intense speculation over links between extremists in Nigeria and northern Mali. Members of Boko Haram are said to have trained with Al-Qaeda's north African branch in northern Mali, but it is unclear whether further ties have been developed.