Troops from the UN's Minusma force came under mortar fire in north-earstern Mali on Thursday evening, resulting in two deaths and 10 injuries, according to the UN.
More than 150 UN troops have been killed in Mali since 2013.
On Sunday about 60 jihadists were killed in the Akabar area, French army spokesman Colonel Patrik Steiger said.
Malian forces sustained "losses" but there were no French casualties, he said.
The French deployed two Gazelle combat helicopters and two Mirage 2000 warplanes in support of their troops but these aircraft did not carry out any attacks, Steiger said.
France's Barkhane force started a reconnaissance and control operation with troops from Mali and Niger and a local militia in Akabar on 28 March, French official said.
The operation took place in "the three-border area" where Mali, Niger and Burkina Faso meet.
This area is known to be used as a haven by the Islamic State in the Greater Sahara, a jihadist group led by Abou Walid al Sharaoui.
During the same period, Barkhane is reported to have launched an attack further west, about 100 km north of Timbuktu
That operating reportedly targeted Abdourahmane al Maghrebi, who is known to train jihadists in the region.
France intervened militarily in Mali in 2013 to help government forces drive al-Qaeda-linked jihadists out of the north.