The Grand Instance Court in Paris ruled in favor of the Union of French Jewish Students, the Jewish Telegraphic Agency reported. Sacha Reingewirtz, vice president of the group, said the company can be fined $1,300 a day for non-compliance.
The order applies only to tweets originating in France.
"It is a major precedent and breakthrough in the attempt to balance privacy online with the need to combat hate speech," Reingewirtz said.
Twitter in a statement said it was reviewing the decision and deciding whether to appeal, The New York Times reported.
"Hate speech," including Holocaust denial, can be prosecuted in France. Last year, there was an uptick in anti-Semitic comments as well as negative remarks about other groups, including Muslims.