Fighter jets, refueling and reconnaissance planes took part in the "major" overnight operation in the Tessalit area north of Kidal, military spokesman Colonel Thierry Burkhard told AFP in Paris.
Kidal is the last bastion of radicals who occupied the desert north for months before France's surprise intervention. Tessalit, near the border with Algeria, is believed to be where seven French nationals captured by Islamists are being held.
Hollande received a rapturous welcome in Mali on Saturday as he promised that France would stay as long as necessary to continue the fight against Islamist rebels in the north.
He told Malians it was time for Africans to take the lead but that France would not abandon them.