Thirty French warplanes on Sunday blasted Islamic extremist training and logistics centres in northeast Mali, just hours after President Francois Hollande visited the country, the military said.
Fighter jets, refuelling and reconnaissance planes took part in the "major" overnight
operation in the Tessalit area north of Kidal, military spokesman Colonel Thierry Burkhard told AFP.
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.
He told Malians it was time for Africans to take the lead but that France would not abandon them.
Malian foreign minister Tieman Hubert Coulibaly said he hoped the French military operation in his country would continue.
"Faced with these hardened fighters whose arsenal must be destroyed, we hope that the mission will continue," he told France's Journal du Dimanche newspaper, adding that the "aerial dimension" of the campaign was particularly important.