The reports in the wake of the Islamist attacks in Paris two weeks ago have been widely derided and prompted Fox to issue an on-air apology for suggesting parts of Paris and the English city of Birmingham were run under Islamic Shariah law.
"A complaint will be filed in the coming days," despite the apology, said a source at Paris city hall.
The news channel broadcast a map outlining the so-called no-go zones, which an expert, Nolan Peterson said felt like Afghanistan or Iraq.
On Saturday a Fox news anchor apologised for "some regrettable errors on air regarding the Muslim population in Europe, particularly with regard to England and France.
"Now this applies especially to discussions of so-called no-go zones, areas where non-Muslims allegedly are not allowed in and police supposedly won't go," the anchor said.
The Fox reports spawned much derision online and saw local news show Le Petit Journal send fake correspondents Mike and John to report on these so-called dangerous areas.
"Oh my God it's an Islamist, he has a beard," one of the jittery reporters cries as a taxi pulls up.
Another takes fright at the sight of a Moroccan restaurant: "Oh my God a couscous! Very dangerous couscous in Paris!"
Asked about the prospect of a lawsuit, Fox News executive vice president Michael Clemente said: "We empathize with the citizens of France as they go through a healing process and return to everyday life.
"However, we find the mayor's comments regarding a lawsuit misplaced."