The initial arrest of 49 soldiers after their arrival at Bamako airport on July 10 sparked a diplomatic row between Mali and its West African neighbor.
Three women in the group were later released.
"Our full support is to the government of Ivory Coast whose soldiers remain detained," French Interior Minister Gerald Darmanin said during a visit to Abidjan where he held talks with Ivorian President Alassane Ouattara.
Ivory Coast says the soldiers were sent on a routine rotation for personnel who provide back-up services for the U.N. peacekeeping mission in Mali, MINUSMA, and has called for their release.
Mali's military-led government says the troops had had no orders or supporting documents and has described them as "mercenaries".
Darmanin also promised France would "continue to help" Ivory Coast fight against terrorism for "Africa's stability."
Relations between France and Mali have been frayed, culminating last month when France pulled its last troops out of Mali, nine years after it was welcomed to help fight a jihadist-fueled insurgency.