Chelsea have begun disciplinary proceedings against midfielder Enzo Fernandez after he posted a video on social media that the French Football Federation said included an alleged "racist and discriminatory" chant.
On Tuesday the FFF said it would file a complaint to world governing body Fifa over the video featuring a song sung by some of the Argentina squad about France's players.
Fernandez's Chelsea team-mate Wesley Fofana, who has one cap for France, posted an image of the video on Instagram, describing it as "uninhibited racism".
Fernandez said he is "truly sorry" for the video he posted as Argentina celebrated winning the Copa America.
"The song includes highly offensive language and there is absolutely no excuse for these words," he said.
"I stand against discrimination in all forms and apologise for getting caught up in the euphoria of our Copa America celebrations.
"That video, that moments, those words, do not reflect my beliefs or my character."
A Chelsea statement read: "We acknowledge and appreciate our player’s public apology and will use this as an opportunity to educate.
"The club has instigated an internal disciplinary procedure."
The FFF will contact the Argentine Football Association (AFA) about live video posted on social media by Fernandez after Argentina beat Colombia 1-0 in the Copa America final on Sunday.
A statement from the FFF, external said president Philippe Diallo "condemns in the strongest terms the unacceptable and discriminatory remarks that were made against the players of the French team".
It added: "Faced with the seriousness of these shocking remarks, contrary to the values of sport and human rights, the president of the FFF decided to directly appeal to his Argentine counterpart and Fifa and to file a legal complaint for racially offensive and discriminatory remarks."
The Argentine FA has been approached for comment.
France beat Argentina in the last 16 of the 2018 World Cup, and Argentina beat France in the final of the 2022 World Cup.
A Fifa spokesperson they were "aware of a video circulating on social media" and "the incident is being looked into".
They added: "Fifa strongly condemns any form of discrimination by anyone including players, fans and officials."
Chelsea have seven France players who are black or mixed race in their first-team squad - Fofana, Axel Disasi, Benoit Badiashile, Lesley Ugochukwu, Christopher Nkunku, Malo Gusto and Malang Sarr.
Chelsea said they find "all forms of discriminatory behaviour completely unacceptable".
They added: "We are proud to be a diverse, inclusive club where people from all cultures, communities and identities feel welcome."