Noel Le Graet has written to the Argentine Football Association to complain about "abnormal" and "shocking" taunts towards France forward Kylian Mbappe.
Mbappe became just the second man to score a World Cup final hat-trick on Sunday, but it was not enough for France as Argentina won on penalties following a thrilling 3-3 draw.
La Albiceleste's third title triumph sparked scenes of wild celebrations back home, with Tuesday's victory parade in Buenos Aires cut short as huge crowds caused the team's bus to be held up.
Amid the celebrations, Argentina goalkeeper Emiliano Martinez – who saved a penalty from Kingsley Coman in the shoot-out – was seen holding a doll with Mbappe's face printed on it.
Social media footage also showed Martinez calling for "a moment of silence" for the Paris Saint-Germain forward in the dressing room after the game, leading former France defender Adil Rami to describe the Aston Villa keeper as "the most hated man in the world of football".
In an interview with Ouest-France, French Football Federation president Le Graet said: "We have launched different procedures. It is very shocking.
"These are boys who have given the best of themselves for the France team to succeed. It is important that we support them.
"I wrote to my counterpart from the Argentine Football Association. I find these excesses abnormal in the context of a sports competition, and I find it difficult to understand.
"It goes too far. Mbappe's behaviour was exemplary."
While Mbappe took his World Cup goal tally to 12 by winning the Golden Boot in Qatar, fellow France forward Karim Benzema missed the tournament with a thigh injury before announcing his international retirement this week.
La Graet was not surprised by the Ballon d'Or winner's decision but refuted suggestions Benzema could have returned to Qatar to feature in the World Cup final.
"He probably intends to focus 100 per cent on his club after having several small injuries," La Graet said.
Asked about reports France considered bringing Benzema back for the final, he added: "To my knowledge, he returned to training very recently, in no case could he have played.
"The staff did the right thing, they wanted him to leave very quickly to see his doctors in Madrid."