The presidency said in a statement that the 26-year-old soldier, from the First Parachute Chasseur regiment, was killed in combat on Saturday evening.
President François Hollande expressed his "profound respect for the sacrifice of this young soldier" and hailed the "courage and ardour" of French forces fighting in Mali.
The government said in a separate statement that the soldier "was mortally wounded during fighting against armed terrorists taking refuge in the Adrar of the Ifoghas [mountains] in northern Mali".
A French helicopter pilot died at the beginning of the French intervention in mid-January and a legionnaire with the 2nd Foreign Parachute Regiment was killed during heavy clashes on 19 February.
Charenton was killed while attacking a rebel position following "several engagements with
terrorist elements", according to military spokesperson Thierry Burkhard.
"The actions aimed to search recesses and tunnels that can be used as shelters," he said, adding that French soldiers seized significant ammunition caches and arms including heavy weapons.
At least 50 members of the Islamist armed group Mujao have been killed and a base destroyed in fighting at In-Manas near the northern town of Gao since Friday, according to Malian military sources.
Chad this weekend claimed that top jihadist leaders Abou Zeid and Mokhtar Belmokhtar have been killed, a development that British Foreign Secretary William Hague said Sunday would be a “blow to terrorism”.