"If it had to be reconsidered, there should not be another vote but we should apply the IOC (International Olympic Committee) jurisprudence, give the gold medal to the silver medallist," the Frenchman told French radio RTL.
"In that case we would go to the United States in 2022," he added, referring to FIFA's 2010 decision to award the tournament to Qatar by a 14-8 margin over the U.S. in the final round of voting.
"But once again, the presumption of innocence must benefit Qatar, too."
Former FIFA deputy general secretary Champagne is one of five candidates bidding to replace the suspended Sepp Blatter at next month's election in Zurich.
Prince Ali Bin Al Hussein of Jordan, Asian Football Confederation (AFC) President Sheikh Salman Bin Ebrahim Al Khalifa, UEFA general secretary Gianni Infantino and South African businessman and politician Tokyo Sexwale are also standing in the vote.
(Reporting by Julien Pretot; Editing by John O'Brien)
