Infantino, who will relinquish his previous role as UEFA general secretary, was voted in on Friday after receiving the backing of 115 federations in the second round of polling at the extraordinary congress in Zurich and will replace disgraced predecessor Sepp Blatter.
Sheikh Salman bin Ebrahim al-Khalifa won 88 votes in round two, with Prince Ali bin al-Hussein and Jerome Champagne taking four and zero respectively. Tokyo Sexwale, the fifth candidate at the start of the day, withdrew prior to the first round.
It was a result which delighted Le Graet, who told fff.fr: "The French Football Federation welcomes the victory of Gianni Infantino as president of FIFA.
"This congress was also an opportunity to review the organisation of FIFA.
"Gianni Infantino and the new governance mark a new era for FIFA, which must start on a better footing and put football at its heart.
"I am sure that Gianni is the man for the job.
"He is a man of action who was able to reconcile the interests of all federations, large or small, within UEFA. I give him my full support and the FFF will be at his service to complete the regeneration of FIFA."