Anti-racism campaigners want Fifa to investigate the abuse of French players, including Paul Pogba, by Russian fans.
Monkey chants could be heard from the crowd in St Petersburg on Tuesday when black French players touched the ball in a friendly against Russia.
The abuse was also audible on a TV broadcast after Pogba scored France's second goal in a 3-1 win.
Piara Powar, head of the anti-discrimination Fare Network, said yesterday: "There should be enough there for Fifa to initiate proceedings."
The Fare Network helps Fifa investigate racism cases, while French sports minister Laura Flessel also called for action.
"Racism has no place on the soccer field," Flessel wrote on Twitter alongside a picture of the French team.
"We should act together at a European and international level in order to stop this intolerable behaviour."
Flessel didn't comment directly on the chants at Tuesday's game.
The case comes before Russia hosts the World Cup in June and July, and Fare said it highlights shortcomings in how the country has prepared for the tournament.
"If photographers heard it pitch-side, then there must have been stewards and other officials who also heard it," Powar said.
"If, toward the end of March, these guys don't know what to do, and they're not initiating procedures and protocols that exist, then that doesn't bode very well for the World Cup. So close to the World Cup, questions are being asked as to why it wasn't dealt with as it occurred during play."
It's the third racism case this season at St Petersburg Stadium, which will host a World Cup semi-final match.
Zenit St Petersburg have twice faced Uefa charges for racism by their fans in Europa League games.
Zenit fans flew a banner praising convicted war criminal Ratko Mladic when playing a Macedonian club in November and are accused of using a racially charged term to mock an injured black player in a game against Red Bull Leipzig.
The second case is due to be heard by Uefa on May 31, two weeks before the World Cup begins.