Loup Bureau was seized by Turkish border guards on the frontier with Iraq in early August after he was found to have photographs and interviews with Kurdish militia fighters among his possessions.
France has been trying to gain consular protection.
Macron told Erdogan he wanted "that our compatriot be able to return to France as soon as possible," according to the statement. The two leaders will discuss the matter again next week.
Turkey considers the Kurdish YPG militia to be an extension of the PKK, which has fought a three-decade insurgency in southeast Turkey and is designated a terrorist organization by Ankara, the United States and European Union.
Macron and Erdogan also discussed the Syrian conflict. The French president reiterated his hopes to pursue a narrow-focused dialogue centered on the fight against terrorism and an inclusive political solution for peace and a unified Syria.
Source: reuters.com