The ambush underscores the fragile security situation in the West African nation as it prepares to go to the polls on July 29.
A spokesman for the French military said there were no deaths among the French troops but it was not known if there were other casualties in the attack, which took place in the restive Gao region.
"French soldiers of the Barkhane military operation were ambushed by terrorists" near the town of Bourem, a Western military source told AFP, referring to the French mission in the country.
A Malian military source confirmed the incident, which came two days after a deadly attack on the Mali headquarters of a five-nation regional force known as G5 Sahel.
Fatouma Wangara, a resident of Gao, said the French convoy was clearly targeted by a suicide car bomb.
"An armoured vehicle blocked the way and the car blew up," she said.
Another resident told AFP that the area around the ambush had been sealed off by French soldiers.
The attack came as over 40 African heads of state are meeting for an African Union summit in the Mauritanian capital of Nouakchott with security high on the agenda.
'Hit the heart' of regional security
On Friday, a suicide attack on the headquarters of the regional Sahel force known as G5 killed two soldiers and a civilian in the Malian town of Savare.
The Al-Qaeda-linked Support Group for Islam and Muslims, the main jihadist alliance in the Sahel, claimed Friday's bombing in a telephone call to the Mauritanian news agency Al-Akhbar.
And on Saturday, four Malian soldiers were killed when their vehicle drove over a landmine in the central Mopti region
Mauritanian President Mohamed Ould Abdel Aziz, whose country is part of the G5 and is hosting the two-day AU summit, warned earlier that security failings were hampering the work of the Sahel force.
He said Friday's attack "hit the heart" of the region's security and lashed out at a lack of international help.
The G5 aims to have a total of 5,000 troops from five nations -- Burkina Faso, Chad, Mali, Mauritania and Niger -- but has faced funding problems.
It operates alongside France's 4,000 troops in the troubled "tri-border" area where Mali, Niger and Burkina Faso meet, and alongside the UN's 12,000-strong MINUSMA peacekeeping operation in Mali.
Mali's unrest stems from a 2012 ethnic Tuareg separatist uprising, which was exploited by jihadists in order to take over key cities in the north.
The extremists were largely driven out in a French-led military operation launched in January 2013.
But large stretches of the country remain out of the control of the foreign and Malian forces, which are frequent targets of attacks, despite a peace accord signed with Tuareg leaders in mid-2015 aimed at isolating the jihadists.
The violence has also spilled over into both Burkina Faso and Niger.
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