"SNCF committed, conspired to commit and aided and abetted others who committed war crimes and crimes against humanity," states the court document, a copy of which was obtained by Agence France-Presse.
"Acting with full knowledge, SNCF was complicit in the commission of genocide."
The class-action lawsuit was filed in US federal court in Chicago on Thursday, which was International Holocaust Remembrance Day.
A Chicago resident and two French citizens are named as plaintiffs in the in the suit. They all had relatives who were sent from France on an SNCF train to Poland's Auschwitz concentration camp, where they died during World War II, AFP reported.
They are seeking compensation for their ancestors' confiscated personal property, which included cash, securities, silver, gold, jewelry, art, musical instruments, clothing and equipment, as well as compensation for the sale of those items.
Those goods were "illegally, improperly and coercively taken from the ownership or control of an individual during the deportations," according to the suit, which also spoke of a "mutually beneficial" relationship between the SNCF and the Nazis.
The plaintiffs are also seeking compensation for third-class train fares billed to the Nazis, even though the victims were packed into cattle cars.
"The Nazis received the human fodder for their Final Solution, as well as the victims' property, all through the collaboration of SNCF," the suit stated.
US federal court has jurisdiction over the matter, the plaintiffs say, because the claims arise under international law enforceable in the Chicago court as federal law, AFP reported.
The suit also claims that the statute of limitations has not expired, even though the deportations took place nearly 75 years ago, because the SNCF only opened some of its archives to the public in 2012.
In December, France agreed to pay $60 million to the United States to be shared among American and foreign nationals deported to Nazi death camps on French trains during World War II.