Serbian-born Dejvid Nikolic, 45, who held French nationality, "fell victim to a suicide attack" about 100 kilometres north of the northern town of Gao in Mali's restive north on Monday, the defence ministry said in a statement.
A suicide bomber in a car targeted French troops who were on a security mission in the Al Moustarat region north of Gao, it said.
Seven soldiers were injured and Nikolic died of his wounds on Monday evening, the statement added.
France kicked off the so-called Serval offensive in January last year to help Malian soldiers stop Al-Qaeda-linked militants and Tuareg rebels from advancing on the capital Bamako from the north of its former colony.
France - which currently has 1,700 soldiers in Mali - had initially planned to end Serval in May and redeploy troops to the Sahel region, but fresh clashes between rebels and the army in the flashpoint northern town of Kidal forced Paris to delay the pullout, which it officially announced on Sunday.
French President Francois Hollande is due to travel to west Africa on Thursday, visiting Ivory Coast, Niger and Chad ahead of the new military mission.
Codenamed Barkhane, it is due to be headquartered in the Chadian capital N'Djamena and is being implemented in partnership with Mauritania, Mali, Burkina Faso, Niger and Chad.