The story by the 23-year-old mother, identified only as Marie-Leonie, created an uproar in France, where the government is trying to combat a rise in anti-Semitic and other hate crimes.
The woman initially claimed she was robbed on a suburban Paris train last Friday by a knife-wielding gang that mistook her for a Jew, scrawled swastikas on her body and cut off a lock of hair.
After police found no clues or witnesses, and learned the woman had a history of lying and filing complaints about assaults that were never proved, the woman was detained on Tuesday for questioning.
In a search of her home in the suburb of Aubervilliers, police found the marker she had used to draw swastikas on her body and the scissors for cutting her hair as well as a credit card she had alleged was stolen, police officials said on Thursday, speaking on condition of anonymity.
The woman "suffers from a need for social acceptance"
The woman's motivation for making up the story was to get out of buying a car, the police officials said.
She told police she felt that if she reported her credit card stolen it would relieve her of the burden of buying the vehicle, the officials said.
A trial date was set for 26 July. In addition to time behind bars she faces a $9,400 fine, said federal prosecutor Xavier Salvat.
During her time in police custody, the woman was examined by a psychiatrist. Salvat said the woman "suffers from a need for social acceptance."