"Noel Le Graet, in the name of the French Football Federation and his executive committee, declares his support for Gianni Infantino," the FFF said in a statement.
It quoted Le Graet as saying the executive committee had voted 11-1 in favour of the move.
"Gianni has all the qualities needed to succeed," the federation head said of Infantino, who is currently general secretary of European football's ruling body UEFA.
He added that the Swiss had shown in working with France's UEFA president Michael Platini, currently subject to an eight-year ban from football, that he had the necessary talent, experience and strength of conviction.
Le Graet said Infantino's manifesto was a step in the right direction for the sport and the federations to restore FIFA's tarnished image as well as develop the sport and its values worldwide.
The FFA announcement came after a heated exchange between Champagne, one of five candidates seeking football's top job as replacement for disgraced Swiss Sepp Blatter, and the FFF chief on Thursday.
Champagne told Reuters that he had met Le Graet to seek his support when 209 national presidents cast their votes in Zurich next month.
Informed that the FFF would be supporting Infantino, Champagne said he told Le Graet that he would protest against his decision at the highest political level.
Former FIFA deputy general secretary Champagne said Thierry Braillard, the Secretary of State for Sports, and Frederic Thiriez, the president of the French Players' Union (LFP), had given him their backing.
Prince Ali bin Al-Hussein of Jordan, Tokyo Sexwale of South Africa and Sheikh Salman Bin Ibrahim Al-Khalifa of Bahrain are the other candidates vying for election on Feb. 26.
The FIFA vote follows the end of Blatter's mandate, with the Swiss caught up in the scandal that has engulfed the world body since last May and which has seen the arrests of 41 associated personnel accused of bribery and corruption.
Blatter and Platini, who had been a strong favourite to succeed him, were banned over a payment of two million Swiss francs ($2 million) made to the Frenchman by FIFA with Blatter's approval in 2011 for work done a decade earlier.
Infantino has become a front-runner as the campaigning picks up pace, securing broad support from European nations as well as in South and Central America.
He will be in Qatar this weekend along with three other candidates.
(Reporting by Alan Baldwin, editing by Ed Osmond)
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