Erdogan repeated an expression Macron had used to describe NATO to hit back at the French leader over his criticism of fellow NATO member Turkey's intervention against Kurdish forces in Syria.
"This is not a statement, these are insults," an Élysee official said, adding: "The ambassador will be summoned to the ministry to explain things."
The official added that France had "no comment to make on these insults."
Macron has been one of the most vocal critics of Ankara's offensive against a Kurdish militia that took the fight to the Islamic State (IS) group in Syria, with the backing of a US-led anti-IS coalition.
During a press conference alongside NATO chief Jens Stoltenberg in Paris on Thursday, Macron said Ankara had presented its NATO allies with a "fait accompli" by launching a military operation "that endangers the actions of the anti-IS coalition."
The comments drew a stinging rebuke from Erdogan during a televised speech on Friday.
"Have your own brain death checked. These statements are suitable only to people like you who are in a state of brain death," Erdogan said.
"You know how to show off but you cannot even properly pay for NATO. You are a novice," he added.
The war of words set the stage for what is likely to be a fractious NATO summit outside London next week, which will be attended by both Macron and Erdogan as well as US President Donald Trump.
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