"With Turkey, we want to resume a responsible dialogue, without naivety and in good faith," Macron wrote on Twitter.
He also said it was important to "assert our European sovereignty" in the Mediterranean to ensure the region's stability, security, as well as biodiversity and the climate.
Macron expressed his solidarity with Greece following the recent major blaze on the Lesbos island, which had destroyed a large migrant camp in Moria.
Earlier on Thursday Macron held a summit with the leaders of Med7 nations, which include France, Greece, Portugal, Spain, Malta, Cyprus, and Italy, on the French island of Corsica. The French president expressed support to Greece and Cyprus in the wake of Ankara's drilling activities in the disputed waters, and reportedly urged the bloc to be tough with Erdogan' government, for what he was condemned by the Turkish authorities.
The subject of the ongoing tensions in the region of Eastern Mediterranean has been Turkey's gas exploration initiative in the areas which Greece and Cyprus claim as their exclusive economic zones. Athens has mobilized its military forces in August amid the aggravation of relations with Ankara, after Turkey had increased drilling operations in the vicinity of the Greek border.
Turkey-Cyprus tensions have been brewing since 2011 over the offshore drilling rights since the discovery of the first gas deposits off the coast of the island in 2011, with Ankara rejecting the EEZ claims of Nicosia.