Fontaine holds the record for the most goals scored by a player at a single FIFA World Cup when he struck 13 times in six games at the 1958 tournament in Sweden.
It was the only World Cup Fontaine played in but he sits joint-fourth alongside Lionel Messi in its all-time top scorers list.
Born in Morocco, Fontaine played for USM Casablanca, Nice and Reims, where he won three league titles, one Coupe de France and finished as runners up in the European Cup in the 1958/1959 season.
Fontaine was forced to retire from football at a tender age of 28 before going on to manage the France national team, Paris Saint Germain, Toulouse and the Morocco national team.
The French Football Federation (FFF) described Fontaine as "the eternal goalscorer" and "a legend of world football".
"The death of Just Fontaine plunges French football into deep emotion and immense sadness," said FFF interim president Philippe Diallo.
"He wrote one of the most beautiful pages in the history of the French team."
"A star of French football, an outstanding striker, a legendary Reims player," said his former club Stade de Reims.
Another of his former clubs, Paris St-Germain, said: "A thought for Just Fontaine. An icon of French football who has left us."
Fontaine won 21 caps for France and scored 30 goals.
