Photographers from news agencies AFP and Reuters said they heard racist abuse -- notably monkey chants -- directed at Ousmane Dembele
and N'Golo Kante. Paul Pogba was also reportedly targeted
after he scored France's second goal in a 3-1 win over Russia in St. Petersburg on Tuesday.
"Racism has no place on the football pitch," France's sports minister Laura Flessel tweeted. "We have to act together on a European and international level to bring an end to this inadmissible behavior."
"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," said the world governing body in a statement sent to CNN.
The Russian Football Union (RFU) has also launched an investigation into the incident, with former player and RFU anti-racism inspector Alexey Smertin telling Russian news agency TASS
: "All details will be thoroughly examined. If violations did take place we will resort to all the necessary measures."
None of the three players on the receiving end of the abuse have commented on what happened, while the French Football Federation did not immediately respond to CNN's request for comment.
FARE did not immediately respond to CNN's request for comment, but on Wednesday the organization's chief Piara Power, told the BBC:
"This is a cause for concern, just over two months before the tournament, with no response from the stadium authorities after what looked to be a major incident."
He added that the "key issue" is that the game took place at one of Russia's World Cup venues, the Krestovsky Stadium in St. Petersburg, which will play host to seven World Cup matches this summer, including one of the semifinals.
'There won't be an incident'
This latest incident is a setback for the RFU and Russia's World Cup Organizing Committee given Smertin told CNN last year he was confident racism would not be an issue at the tournament this summer.
"It won't be," he said ahead of the 2017 Confederations Cup. "There won't be an incident. The people who know me, they know how honest I was on the pitch. Why should I lie?"
Over recent years, several black players have reported incidents of racist abuse during games in Russia, although data provided by FARE and Russia-based SOVA shows that some -- albeit limited -- progress has been made, with the number of reported cases of discrimination falling from 101 in 2015-16 to 89 in 2016-17.
Earlier this month, Russian Premier League champions Spartak Moscow were handed a suspended stadium ban by the RFU after Lokomotiv Moscow goalkeeper Guilherme Marinato was subjected to persistent racist abuse.
Meanwhile, Moscow will play host to a high-profile Europa League quarter-final on 12 April, as Arsenal travel to CSKA Moscow amid various concerns over UK-Russia political tensions
, fan violence, and -- even more so now -- racist abuse.