"Both leaders emphasised the importance of fostering economic and trade relations as well as mutual investments," the source told the French news agency AFP.
They also agreed on a meeting between the two countries' finance ministers "as soon as possible".
Macron, a former investment banker, apparently stressed the importance of Turkey's economic stability, after several days of international market worries about the lira's fall, runaway inflation and a big current account deficit.
Lira falls, inflation soars
The lira has fallen 40 percent against the dollar this year and annual inflation is estimated at 101 percent.
The president has also come under fire for putting pressure on the central bank not to raise interest rates, a measure most economists deem vital to curb inflation.
This month the crisis has worsened as US President Donald Trump has sanctioned Turkish government officials and doubled already existing steel and aluminium tariffs over the house arrest of US pastor Andrew Brunson, who is accused of links with PKK armed Kurdish separatists and Fehtullah Gulen, the Pennsylvania-based imam alleged to be behind the 2016 coup attempt.
Erdogan seeks new partners
Erdogan has responded with tariffs on some US goods.
He has also sworn to develop new partnerships, meeting Russian Foreign Affairs Minister Sergey Lavrov this week and floating the idea of meetings with German and French representatives.
Qatar on Wednesday promised to make a 15 billion-dollar (13 billion-euro) direct investment in Turkey
Finance Minister Berat Albayrak, Erdogan's son-in-law, was due to address hundreds of foreign investors through a teleconference on Thursday, in an apparent attempt to reassure the markets.