Champagne, who held four different posts at FIFA, including deputy secretary general, between 1999 and 2010, said the organisation was "in danger" after being buffeted by a wave of scandals over the last few years.
"We need to save FIFA and its role of governance and redistribution, which is in danger at a time when they are needed the most," said Champagne in a letter to FIFA's 209 member associations, which will choose the next president at a Congress on Feb. 26.
Earlier this month, Blatter and UEFA president Michel Platini, who had been the favourite to replace him, were both suspended for 90 days pending an ethics investigation.
Champagne had wanted to run in the election earlier this year but failed to get the written backing from five national football associations (FAs) which is needed to register.
With the Oct. 26 deadline for nominations looming, Jordanian Prince Ali Bin Al Hussein and former Trinidad and Tobago midfielder David Nakhid have announced their candidacies.
Champagne confirmed to Reuters that he had the five FAs, said he would not comment on rival candidates and criticised the way in which the campaign had been conducted.
Champagne has also been a consultant for the Cyprus Turkish Football Federation during their move to apply for KOP Cyprus Republic Football Federation membership.