The attack was launched Wednesday in the city of Gao at the camp shared by government forces and armed groups, who had signed a peace deal in 2012 and were to carry out joint patrols.
The Al Mourabitoun militant group claimed it was behind the attack in a statement posted on Facebook and obtained by Mauritanian news agency Al-Akhbar.
The group is the Mali branch of Al Qaeda's North African affiliate, Al Qaeda in the Islamic Maghreb (AQIM).
"We will not allow the establishment of military posts and headquarters or the convening of patrols and convoys belonging to the French occupiers to wage war against the mujahideen," the statement read.
Al Mourabitoun is led by terrorist Mokhtar Belmokhtar, who is believed to have been behind a number of high-profile attacks against military and civilian targets in Mali and elsewhere in Africa.
The one-eyed Belmokhtar has been mistakenly declared dead many times.
The United States named him a global terrorist 12 years ago and offered a $5 million reward for information about him.
Francois Delattre, France's ambassador to the United Nations, said Wednesday that the attack was an "attempt against the ongoing efforts in Mali to stabilize the country and a direct effort to undermine the peace agreement
Mali is a former French colony that has struggled with instability and Islamist extremists for years.
An uprising by rebels from the Tuareg ethnic minority began in the country's sparsely populated north in January 2012, followed by a military coup two months later. During the chaos that followed, Islamist extremists who had helped the Tuareg against Malian forces took over a large portion of northern Mali for themselves.
At Mali's request, France sent thousands of troops after the coup to help push out the militants. The United Nations also established a peacekeeping mission to secure the government enough to continue a peace process.
French troops helped push the militants out of urban areas, but the militants persisted in the nation's desert regions.
An Algerian-brokered peace deal, which allowed for greater autonomy in the country's north, was signed in June 2015 by the so-called Coordination of Movements of Azawad, representing the Tuareg-led rebels.