Neither President Francois Hollande's office nor the Foreign Ministry could confirm the death of Gilberto Rodriguez-Leal with certainty. Rodriquez-Leal had been held since November 2012.
News of his probable death followed a report today by the Agence France-Presse news agency. AFP said a telephone call from the Mujao terrorist group said it had killed Rodriguez-Leal.
Hollande's office said in a statement that France would "do all to uncover the truth ... And will not leave this unpunished."
The president's office said it suspected that poor detention conditions, rather than an execution, were to blame. France intervened in Mali in 2013 to rout Islamist extremists. Two other hostages have died.