The French foreign ministry in a notice urged citizens in the far north of Cameroon, where the kidnapping took place, "to leave the area as quickly as possible" and advised against travel to areas bordering Nigeria until further notice.
Boko Haram fighters have been spotted in northern Cameroon on several occasions.
Another group, Ansaru, which criticises Boko Haram for including Muslims among its victims and targets non-believers, last weekend claimed responsibility for the kidnapping of seven foreign employees of a Lebanese company operating in Nigeria and linked the act to France’s intervention in Mali.
It is not known how many French nationals are in the area but 6,200 are registered as living in Cameroon.
The family - a couple, their children aged five, eight, 10 and 12 and an uncle - were snatched near the Waza nature reserve by six gunmen on three motorbikes on Tuesday.
Their vehicle was later found in a river neat the border with Nigeria.
Cameroonian officials have confirmed reports that they had been taken across the border into Nigeria and police in both countries are investigating the affair.
French gas company GDF Suez said on Tuesday that the father is one of their employees and that the family lived in Yaoundé.
"We believe that the Boko Haram sect carried out this kidnapping, but we don't yet have a claim of responsibility," Le Drian told France 2 television. "These are groups that claim the same fundamentalism, who use the same methods, whether it's in Mali, Somalia or Nigeria."
The French foreign affairs ministry says on its website that France and Nigeria’s involvement in the Mali conflict have “given rise to explicit threats against French interests and expatriates”.