The FFF said on Thursday the executive committee decision was unanimous.
The FIFA presidential election is scheduled for March.
"Whilst support had initially been given to the FIFA president, who was then the sole candidate for his own succession, the conditions for that support are no longer met," the FFF said.
"A series of events directly involving FIFA's governance and its president, and in direct conflict with the fundamental principles of good governance and the values of football, occurred after the FFF expressed its support on June 29."
The French cited Infantino's plan to sell stakes in the World Cup to private equity for $US4.2 billion ($A5.86 billion).
FIFA withdrew the proposal on August 1, just days after it was made public, following intense pushback.
"Today, whilst this project has been definitively abandoned thanks to a concerted response within UEFA in conjunction with several other confederations, the issue of FIFA's governance cannot be considered resolved," the FFF said.
It added Infantino's recent initiatives have "seriously damaged the image and unity of football".
UEFA has led the calls for Infantino to go, saying it lost confidence in him and previously threatened to boycott FIFA tournaments, including the World Cup.
Several national associations, including England, have withdrawn support for Infantino's re-election.
FIFA said on Sunday that Infantino plans to stand again in next year's elections for a final term in office through 2031.
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