Platini, the head of European soccer's governing body UEFA, is currently suspended along for 90 days along with FIFA president Sepp Blatter as soccer's governing body.
Swiss authorities are investigating the decision to award the 2018 and 2022 World Cup tournaments to Russia and Qatar respectively and the United States Department of Justice has indicted 14 soccer officials and sports marketing executives on a series of corruption charges.
Since 2010, FIFA's own Ethics Committee has banned more than one dozen current and former members of the executive committee, either while in office or after they had left.
FIFA said that Platini's bid would not be processed while he is banned, but he could still stand if he wins an appeal.
"Should such a ban be lifted or expire before the FIFA presidential election, the Ad-hoc Electoral Committee would decide, depending on the respective exact point in time, on how to proceed with the candidature concerned," said FIFA in a statement.
As an alternative European candidate, UEFA's general secretary Infantino announced he would stand on Monday.
Champagne is a former French diplomat who held various posts at FIFA betweeen 1999 and 2010, but is a critic of UEFA.