'Dear Tayyip': Macron and Erdogan exchange letters
Erdogan wrote a New Year message to Macron expressing condolences for several attacks in France last year, Turkish Foreign Minister Mevlut Cavusoglu was quoted as saying by local media.
Macron sent back a "very positive" letter this week, starting with the greeting "Dear Tayyip" and saying he was open to a meeting, Cavusoglu said.
The French presidency confirmed the exchange of letters without providing details.
"We now need tangible gestures" from Ankara, the French presidency said.
Ankara and Paris last year sparred over a host of international issues, including the conflicts in Syria, Libya and Nagorno-Karabakh.
The European Union is now drawing up an expanded list of Turkish individuals to sanction for Ankara's decision to drill for natural gas in eastern Mediterranean waters near Cyprus.
The diplomatic tensions have been accompanied by a bitter personal feud between the two men.
Erdogan last year accused Macron of "Islamaphobia", suggested he undergo mental health checks, and urged French voters to "get rid of Macron as soon as possible".
Macron, for his part, remarked at a meeting with EU leaders that Turks "deserve something else" than the policies of Erdogan.