Olympic 100m champion and her boyfriend, 100m world record holder Tim Montgomery, are both working with the Canadian.
Francis coached Ben Johnson when he won the 100m title at the Seoul Olympics only to be stripped of gold for testing positive for drugs.
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Their association with Francis will only serve to further hurt the sport
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Michael Johnson
Five-time Olympic gold medallist Johnson said in his column for the Daily Telegraph: "I cannot understand why anyone would choose Francis as a coach.
"He admitted he encouraged Ben Johnson to take steroids and his publicly stated position that no athlete can be successful without the use off drugs.
"But I am even more puzzled by Marion's decision to employ him as a coach.
Ambassadors
"She is the most high-profile athlete in the entire sport and has been very highly respected by the media and most who follow athletics."
Johnson added: "Jones and Montgomery, to a slightly lesser degree, are the ambassadors of this sport.
"They have both failed in that responsibility and have obviously chosen to ignore it.
"Their association with Francis will only serve to further hurt the sport from a public perception and a sponsor perspective.
"Everyone else can see this so clearly, but I scratch my head wondering why Marion can't," added Johnson.
Francis was banned in 1989 from coaching members of Canada's national team after he admitted giving steroids to Johnson and other athletes.
But in the statement issued on Friday, he insisted that he no longer "encouraged, nor condoned the taking of banned performance-enhancing substances by any of the athletes who have consulted me".