The air strikes targeted “logistical depots and training centres” run by armed Islamist groups in the border area, spokesperson Thierry Burkhard said Sunday.
Hollande finished his visit to Mali on Saturday with a speech in the capital Bamako.
He said that French troops will stay “as long as it takes” to restore northern Mali to control by the Malian government.
Thirty aircraft, including refuelling and reconnaissance planes, were involved in the operation, he said.
The militias are believed to have taken refuge in the region, notably in the Ifoghas mountains, which were the birthplace of the Tuareg separatist campaign for Azawad.
The seven French hostages held captive by Al Qaida in the Islamic Maghreb (Aqim) and its allies are probably in the region, Paris believes.
The captors threatened to kill the hostages if French combat troops set foot on Malian soil.