"FIFA urges all member associations leagues, clubs and disciplinary bodies to adopt the same procedure, as well as a zero-tolerance approach to incidents of racism in football, and to apply harsh sanctions for any such kind of behaviour," Infantino said in a statement.
The abuse levelled at Gouano in Friday's goalless draw comes after rising Italy star Moise Kean was racially abused by Cagliari fans earlier in the month, while Inter Milan fans took aim at Napoli defender Kalidou Koulibaly in December.
England players were also subjected to monkey chants during a Euro 2020 qualifier in Montenegro and there have been a series of episodes involving London clubs.
"FIFA stands together with Prince Gouano, Kalidou Koulibaly, Raheem Sterling, Danny Rose, as well as any other player, coach, fan or participant in a football match who has suffered from racism, whether at the highest professional level or in a school playground," Infantino added.
Ligue 1 match temporarily stopped due to racist chants
The clash in Dijon was halted in the 78th minute as players from both sides stopped playing and headed towards the touchline after Gouano said he heard insults.
"It's over," Gouano said. "We're not playing on. I'm taking off my team-mates."
Players, including Gouano, went to remonstrate with fans, while referee Karim Abed also asked the stadium announcer to "get the message across, if it happens again, we stop".
Following discussions between players, coaches and officials, play then resumed.
"In Dijon, we saw that it was an isolated supporter who could be identified and arrested," football sociologist Nicolas Hourcade, a professor at the Central School of Lyon, told AFP.
"In other countries, there are collective demonstrations where a whole section of the ground, or a good part of one, can shout monkey chants or racist slogans."
After the game, the French football league (LFP) said it would investigate and also announced that Dijon had identified the culprit. The club said they intended to press charges.
"These disgusting shouts are contrary to the values conveyed by sport, they insult our Republic, and I welcome the rapid reaction of the LFP: racism will never have a place in France," responded Interior Minister Christophe Castaner.
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Anti-racism campaigners urge abandoning matches.
"It's very important to stop. It points out that there is something that is not in the spirit of football," former France captain Lilian Thuram told Europe 1 radio.
"When you watch the matches, particularly in Italy, the presidents and referees act as if they hadn't heard."
The ugly scenes in Cagliari on April 2 when Kean, along with Blaise Matuidi and Brazilian Alex Sandro, were targeted by monkey noises and jeers throughout the match, came after Matuidi suffered similar abuse at the same ground last year.
Instead of denouncing their fans, Cagliari's leadership blamed Kean for celebrating his late winner by standing motionless and silent with arms spread in front of the hostile stand.
"Italy is a case apart for two reasons," Hourcade said. "The historical strength of the extreme right, and the presence of openly fascist fan organisations."
But in England too, there have been numerous recent incidents at all levels of football.
On Thursday, half a dozen Chelsea fans posted a video on social media in which they sang that Liverpool's Egyptian star, Mohamed Salah, was a "bomber". Chelsea identified and barred three of the fans.
Arsenal are attempting to identify a fan who was caught on video shouting racist abuse at Napoli's Koulibaly in a Europa League game on Thursday.
In December, Manchester City's Raheem Sterling was the target of insults at Chelsea and a Tottenham fan threw a banana in the direction of Arsenal's Pierre-Emerick Aubameyang.
One of the major issues is "to identify the perpetrators of these acts to punish them," said Hourcade.
Spurs' England defender Rose has blasted the game's rulers for failing to rein in racism, calling their efforts "a farce".
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