The Jewish Students’ Union of France (UEJF), one of the groups that brought the case against Twitter, welcomed the decision on Thursday afternoon.
"We're not able to identify the individuals, only Twitter can do so,” said vice-president Sacha Reingewirtz.
His organisation is waiting to see how Twitter applies the court's decision, he said, adding that some opponents responded with more abuse.
"We've already tweeted the decision,” he explained. “And we see on Twitter that the decision has apparently triggered a new rise of anti-semitic messages directed against our organization, so there is still work to be done, both by us and Twitter, but we're happy the French justice is now changing the way it is."
“If Twitter does not live up to its obligations, we will return before the same magistrate and demand Twitter’s conviction and financial penalties,” said the groups’ lawyer Stéphane Lilit.
The case was launched last October when the UEJF and other organisations sounded the alarm over anti-Semitic and racist tweets, many using the hashtag #UnBonJuif (#AGoodJew).
Since then others have pointed to homophobe tweets using the hashtag #SiMonFilsEstGay (#IfMySonIsGay).
At the beginning of the year the government started discussing with Twitter how to combat the hate message trend.
A first meeting with Women’s Rights Minister Najat Vallaud-Belkacem, Twitter executives and campaign groups is planned for 8 February at the women’s rights ministry.
A year ago Twitter set filters in various countries.
The first one was used in Germany last October to block messages by a banned far-right group in Hanover.