The US network claimed there were "no-go areas" in the French capital where police and non-Muslims refused to go.
Anne Hidalgo said the people of Paris had been "insulted" and the city's image had been "damaged".
The network has since apologised for making "regrettable errors" on air regarding the Muslim population.
Ms Hidalgo told CNN: "When we're insulted and when we've had an image, then I think we'll have to sue. I think we'll have to go to court, in order to have these words removed.
"The image of Paris has been prejudiced, and the honour of Paris has been prejudiced."
Her words were echoed by the deputy mayor, Patrick Klugman.
In an interview with the BBC he said Ms Hidalgo was "definitely serious" about her intention to sue Fox News.
"We have our legal advisers working on the case," he added. "We are looking under which jurisdiction to bring the case, Paris or New York."
In response to Ms Hidalgo, Fox News executive vice president Michael Clemente said: "We empathise 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."
Fox has also apologised for comments by terror expert Steven Emerson, who claimed Birmingham was "totally Muslim" and ruled by Sharia law.
Fox News host Jeanine Pirro subsequently said Emerson had "made a serious factual error that we wrongly let stand unchallenged and uncorrected".
Mr Emerson said he had made an "inexcusable error".
Prime Minister David Cameron responded by calling him "a complete idiot".
In another apology over the weekend, Fox News presenter Julie Banderas said the channel had "made some regrettable errors on air regarding the Muslim population in Europe", and apologised "to any and all who may have taken offense, including the people of France and England".

Jack Lopresti said a letter sent to party members calling for a new candidate was part of an "attempt to destroy my character and reputation".
The Filton and Bradley Stoke MP left his wife for fellow MP Andrea Jenkyns, who gave birth to their son in March.
Mr Lopresti was reselected at a meeting on Friday evening.
An anonymous letter sent to Conservative Party members in the constituency earlier this month said there were "many of us who feel very strongly that Mr Lopresti is not representing our constituency in a very good way".
It added there were "several excellent people" who should be given the chance to become the prospective parliamentary candidate.
The local party has reacted to the letter by writing to party members assuring that "appropriate legal action" would be taken if the writer was identified.
He was first elected in 2010 and re-elected with a near-10,000 majority five years later.
In November last year, it was reported he had become engaged to Ms Jenkyns â€” who ousted former Labour shadow chancellor Ed Balls to become MP for Morley and Outwood in 2015. Their son, Clifford George, was born in March.
"For the last month my family and I have been subject to a vicious smear campaign with racist overtones," he said.
"Since the day after my son Clifford was born, my office has been bombarded with bogus calls from people purporting to be national journalists and with dark threats of illegally taped conversations. This has deeply upset my staff.
"I have had many messages of support from party members and lots of constituents, and I am sure that this recent attempt to destroy my character and reputation has been orchestrated by a small handful of people.
"I can only think that this is as a result of personal choices I have made in my private life, which some may not have approved.
"I love my fiancee Andrea and am extremely proud of my young son Clifford and nobody will ever be able to change that."
The mayor of Paris has said she will sue Fox News for its inaccurate reporting about the city following the attack on the magazine Charlie Hebdo.
[NEXT_CONCEPT]
A Conservative MP who faced deselection by his own party has blamed a "vicious smear campaign" against him following revelations about his private life.