"FIFA is aware of a video circulating on social media and the incident is being looked into," a spokesperson for world football's governing body said.
They added: "FIFA strongly condemns any form of discrimination by anyone including players, fans and officials."
The chants were heard during a live video posted on social media by Chelsea and Argentina midfielder Enzo Fernandez from the team bus in the wake of the Copa victory over Colombia in Miami on Sunday.
Some players, including 23-year-old Fernandez, sing a chant dating back to the 2022 World Cup final in which Argentina beat France.
The song targets France's star striker Kylian Mbappe among others and includes racist and homophobic insults.
Chelsea had earlier announced they had launched an internal disciplinary procedure against Fernandez over the incident.
Fernandez has apologised and the club said in a statement it had launched an "internal disciplinary procedure."
"Chelsea Football Club finds all forms of discriminatory behaviour completely unacceptable," it added.
"We acknowledge and appreciate our player's public apology and will use this as an opportunity to educate."
Fernandez, who joined Chelsea from Benfica for a Premier League record fee of £105 million ($136.8 million) in 2023, said in his apology: "The song includes highly offensive language and there is absolutely no excuse for these words.
"I stand against discrimination in all forms and apologise for getting caught up in the euphoria of our Copa America celebrations."
The French Football Federation (FFF) complained to FIFA about the chants on Monday.
FFF president Philippe Diallo "condemned with the greatest firmness the unacceptable racist and discriminatory remarks made against players of the France team".
France beat Argentina in the last 16 of the 2018 World Cup.
