Defender Schmelzer misses out with an ankle problem, midfielder Goetze has a flu virus and Reus picked up an adductor muscle injury in Sunday's 3-2 victory over Bayer Leverkusen.
Bayern Munich midfielder Bastian Schweinsteiger also pulled out on Saturday.
Ilkay Gundogan, despite an ankle injury Sunday, will link up with the team coach Joachim Low later in preparation for the trip to Paris.
Lazio striker Miroslav Klose could face up to two months on the sidelines after suffering a knee injury in his side's 3-2 defeat to Genoa on Saturday.
Leverkusen forward Andre Schurrle is likely to be involved, though, and cannot wait.
"It is definitely going to be a cool game in Paris," he said on the website of the German Football Association (DFB).
"Games against France are always great. I can't wait."
The withdrawals raise doubts about how important a friendly is in February -- a month before Germany's next World Cup qualifying matches.
However, Schurrle claims it is an important warm-up for those games and a date that Germany cannot do without if it is to be ready in March.
"Of course it's an important game," he said. "It is the first game of the new year and an important meeting. We have got to face good sides to fine-tune our movements before we get involved in World Cup qualifiers.
"Then, we are going to have to show who is the number one in the group."