Defender Schmelzer is out with an ankle problem, midfielder Gotze has a flu virus and Reus picked up an adductor muscle injury in Sunday's 3-2 victory over Bayer Leverkusen, German FA spokesman Jens Grittner told a news conference on Monday.
Grittner said another Dortmund player, midfielder Ilkay Gundogan, would make the trip despite a minor injury. He also added there were fitness doubts concerning defender Lars Bender and striker Miroslav Klose.
Bayern Munich midfielder Bastian Schweinsteiger had already been ruled out of Wednesday's game with a minor knock.
The spate of withdrawals are a worry for Germany who have lost five of their last six meetings with France and last beat Les Bleus in August 1987.
"Records are there to be broken," said manager Oliver Bierhoff. "A win would be a good morale boost for our team."
Coach Joachim Low is set to start with in-form Hamburg SV keeper Rene Adler instead of first-choice Manuel Neuer.
Adler lost his starting spot to Neuer after sustaining a rib injury ahead of the 2010 World Cup and has not played for his country for more than two years.
"I am happy to be part of the team again," he said. "It is a sensational experience because I know how quickly things can change."
