President Ilham Aliyev pardoned a total of 20 people on Wednesday, citing their "personal qualities, health status, family circumstances" and other reasons, according to a statement.
The Frenchman was arrested as relations between Baku and Paris deteriorated because of France's support for Armenia, which has long been in conflict with Azerbaijan.
France describes the pardon as the result of "patient" dialogue.
The announcement comes a day after Russian-Uzbek oligarch Alisher Usmanov was removed from the EU's sanctions list against Russia, at France's request. A senior diplomat in Brussels told AFP that France had pressed the issue as part of a possible deal with Azerbaijan on prisoners.
It is unclear what connection Usmanov would have to Azerbaijan in that case.
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