Chelsea are looking into a video shared on social media by midfielder Enzo Fernandez, which the French Football Federation claims contains an alleged "racist and discriminatory" chant.
The FFF said that it would submit a protest with the international regulatory body Fifa over a video, including a song sung by several of Argentina's players who are denigrating French players.
Fernandez's Chelsea teammate Wesley Fofana, who has one cap for France, described the video as "uninhibited racism" on Instagram.
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Chelsea is investigating and takes the situation seriously.
The FFF will also approach the Argentine Football Association (AFA) regarding a live video uploaded on social media by Fernandez as Argentina celebrated winning the Copa America by defeating Colombia 1-0.
According to an FFF statement, President Philippe Diallo "condemns in the strongest terms the unacceptable and discriminatory remarks that were made against the players of the French team."
The statement continued: "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 Football Association has been sought for comment.
France defeated Argentina in the 2018 World Cup round of 16, and Argentina defeated them in the 2022 World Cup final.
