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Chelsea are investigating a video posted on social media by midfielder Enzo Fernandez which the French Football Federation says includes 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".
BBC Sport understands Chelsea are investigating the incident and treating it seriously.
The FFF will also contact the Argentine Football Association (AFA) about live video posted on social media by Fernandez as Argentina celebrated winning the Copa America, after beating Colombia 1-0 in the final on Sunday.
A statement from the FFF, external said that 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, before Argentina beat them in the final of the 2022 World Cup.