The world governing body said in a statement it was “collecting the different match reports and potential evidence” of the discrimination.
Manchester United’s Paul Pogba and Barcelona’s Ousmane Dembele are said to be among those subjected to taunts.
The match was played at the Krestovsky Stadium in Saint Petersburg, a host venue at this summer’s World Cup.
French Minister for Sport Laura Flessel said: “Racism has no place on the football pitch. We have to act in unison at a European and international level to put an end to these inadmissible actions.”
French minister Laura Flessel is a two-time Olympic fencing champion
The issue was first reported by photographers from news agency AFP,who said they heard chants when players went to take corners.
It is the latest in a number of incidents of discrimination linked to Russia.
The FARE (Football Against Racism in Europe) network monitors discrimination in football on a national scale and detailed close to 90 incidents of racism in the Russian league last season.
Piara Powar, head of the organisation, feels the actions that marred France’s win raise concerns about fan and player safety during the World Cup.
“For us, the key issue is that the match took place at a stadium that will host one of biggest games during the World Cup, a semi-final will be there, plus many group games,” he told BBC Sport.
“In many ways this match was a test of the protocols that the Russian FA has put in place, it was a match governed by the Russian FA.
“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.”
Fifa said it was taking into account evidence from the “FARE observer who was present at the game”.