Manchester United midfielder Paul Pogba and Barcelona forward Ousmane Dembele were among those said to be targeted by monkey noises during a friendly against the World Cup hosts in St Petersburg on Tuesday.
Pogba and Dembele are yet to comment on any racist chanting in the 3-1 win for Didier Deschamps' side but FIFA confirmed it is gathering evidence.
"FIFA is collecting the different match reports and potential evidence in regards to the discriminatory incident reported in the media, including the one from the FARE [Football Against Racism in Europe] observer who was present at the game," a FIFA spokesperson said.
"Please understand, until we have evaluated all information available, we cannot comment further."
French sports minister Laura Flessel called for action to be taken on an "international level".
"Racism has no place on the football pitch," Flessel wrote on Twitter alongside a photo of the France team lining up before a game.
"We should act together at a European and international level to stop this intolerable behaviour."
« Le racisme n’a pas sa place sur les terrains de football. Nous devons agir de concert au niveau européen et international afin de faire cesser ces comportements inadmissibles » #FRARUS #exaequo .— Laura Flessel (@FlesselLaura) March 28, 2018
Crédits FFF/ Bastien Lheritier. pic.twitter.com/kRB1fbBNjO
Last week UEFA opened disciplinary proceedings against Zenit - whose Krestovsky Stadium hosted the France friendly - after racist chants were allegedly heard during a Europa League game against RB Leipzig.
Lord Herman Ouseley, chair of Kick It Out, said there is a need to clamp down on racism in the country ahead of the World Cup.
"In light of this alleged incident, the French Football Federation must take strong action in raising this issue with FIFA and other football authorities, including the FARE network," he told Omnisport in an emailed statement.
"The football authorities must understand that a lack of effective action against the issue of racism in Russian football will likely result in the further abuse of black players in matches involving the country.
"Kick It Out also believes the Football Association should ensure it provides increased protection from racial abuse for England's black players and supporters during this summer's FIFA World Cup."