The United States Anti-Doping Agency has banned Armstrong for life and taken away his titles won between 1999 and 2005 after accusing him of being involved in an elaborate doping conspiracy.
"When you read the USADA report, you can't be indifferent," Prudhomme said. "It depicts an era and a system which are forever soiled. The best solution is to say that there should be no (Tour) winner those years."
Although the majority of Tour podium finishers at that time were implicated in doping scandals, Prudhomme believes that the sport has subsequently changed for the better.
"It is in that period that the fight against doping was built and made huge progress," he said. "Today's cycling is different."
The International Cycling Union will decide whether to officially erase Armstrong's name from the Tour records. UCI president Pat McQuaid said on Friday the world governing body's lawyers would come up with a response to USADA's 1,000-page file within 21 days after its receipt.