Earlier this week, a purported leaked email from Nice's former sporting director Julien Fournier accused Galtier of complaining about the amount of black and Muslim players in his Aiglons squad.
The Frenchman was only in charge of Nice for the 2021-22 season before departing for PSG, and journalist Romain Molina first reported the email sent by Fournier to Dave Brailsford, a director at Nice's owners Ineos.
Fournier claimed that Galtier had wanted to rid the club of several black and Muslim players in his squad, with the likes of Amine Gouiri, Hicham Boudaoui, Mario Lemina, Jean-Clair Todibo and Youcef Atal not wanted at the Allianz Riviera by the manager.
Fournier also alleges that he pitched the idea of signing Ozan Kabak from Schalke, but Galtier vetoed the move after learning of the centre-back's Turkish nationality.
Galtier is said to have taken issue with players fasting during Ramadan, despite being presented with scientific data proving that it had little effect on their physical levels.
The 56-year-old's lawyer has already stated that Galtier "firmly denies" the accusations against him, and he addressed the media in Friday's press conference before the weekend's Ligue 1 clash with Lens.
Before taking any questions from reporters, Galtier insisted that he will not allow his and his family's name to be "sullied", and he has faith in the judicial system to clear his name.
"I am deeply shocked by the comments attributed to me and which have been relayed by some in an irresponsible way," Galtier is quoted as saying by The Athletic.
"They hit me in the depths of my humanity. I am a child of a low-income housing estate (HLM), raised in diversity, and the values of sharing and respect for others, whatever their origin, colour or religion. My whole life as a man, as a footballer and then as a coach, has been dictated by the concern for, and sharing and living well with, others.
"I cannot accept that my name and my family be sullied in this way. I therefore have decided to take legal action against anyone who harms my reputation. I can only be satisfied with the opening of a legal investigation.
"I have confidence in the justice system of my country. In order to allow justice to follow its course, I will not make any further comments on this subject. Paris Saint-Germain have a very important match to play this Saturday. All my energy and my concentration are turned towards this objective."
PSG also released their own statement expressing support for their head coach, who is also understood to be the subject of an internal investigation from president Nasser Al-Khelaifi.
"Serious allegations have been made in the media against our coach Christophe Galtier. Christophe responded clearly by firmly denying them and announcing that he was going to take legal action. The club supports Christophe Galtier after the numerous and unacceptable threats he has received and now wants the truth to be established by justice," the statement read.
"While waiting for the conclusion of the judicial process, and in order to protect the safety of all, the club calls on everyone to take responsibility and to calm down."
PSG welcome Lens to the Parc des Princes for a top-of-the-table clash on Saturday evening, with the champions six points clear of Franck Haise's side at the summit.