The video, posted by Argentina international Fernandez on his Instagram account, featured a song sung by some of the Argentina squad about France's players.
The midfielder later apologised for the video where Argentina players were celebrating winning the Copa América after beating Colombia 1-0 in Sunday's final.
"The song included highly offensive language and there is absolutely no excuse for these words," Fernandez said on Instagram.
"I stand against discrimination in all forms and apologise for getting caught up in the euphoria of our celebrations. That video, that moment, those words, do not reflect my beliefs or my character."
The French Football Federation (FFF) said the video included an alleged "racist and discriminatory" chant and that it would file a complaint to global football's governing body FIFA.
"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 Argentinian counterpart and FIFA and to file a legal complaint for racially offensive and discriminatory remarks," the FFF said.
France international Fofana commented on the video on social media platform X, writing: “Football in 2024: uninhibited racism." The comment was accompanied by a clip from the video.
FIFA and the Argentinian Football Association did not immediately respond to requests for comment. British media reported that Chelsea were investigating the video.
France striker Kylian Mbappe and other players of African descent on the national team received racist abuse after they lost to Argentina in the 2022 World Cup final, prompting a senior French cabinet member to call for a FIFA investigation.
Argentina beat Colombia to collect a record 16th Copa América title on Sunday.
