The fight, involving a group of about 60 jihadists, took place on Sunday in the Akabar area, spokesman Colonel Patrik Steiger said, adding that Malian forces sustained "losses" but there were no French casualties.
French commandos and Malian forces began a "reconnaissance and control operation" in the Akabar region on 28 March, working in liaison with the Nigerian army and a local self-defence group, Steiger said.
"On 1 April, they were confronted by an ATG [armed terrorist group] estimated to number 60 individuals, around 90 kilometres south of Menaka and three kilometres from the Nigerien border," he said.
The border zone is used as a haven by the jihadist group Islamic State in the Greater Sahara (ISGS), 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 intervened militarily in Mali in 2013 to help government forces drive al-Qaeda-linked jihadists out of the north.
The initial mission was followed in 2014 by Operational Barkhane, which deployed 4,000 French troops alongside the UN's 12,000-strong MINUSMA peacekeeping operation in Mali.
The insurgency however has spread to central and southern Mali and spilled into Burkina Faso and Niger, prompting plans to create a joint anti-terror force among five Sahel countries, also including Chad and Mauritania.