The Paris appeal court ordered Twitter to provide information about "racist or anti-Semitic" tweets to a Jewish students' group and four anti-racist campaigns, backing up a lower court's decision in January.
Twitter had failed to comply and failed to provide a reason for not doing so, the appeal court ruled, dismissing conditions that the company had placed on its compliance.
Twitter has also failed to create an "easily accessible and visible" means for users to notify "illicit" content, it added.
This week government spokesperson Najat Vallaud-Belkacem criticised Twitter for allowing users to open fake accounts in the name of dead anti-fascist Clément Méric, which sent sick jokes, such as "got a headache".
Assuming someone's identity is punishable by a year in prison and/or a 15,000-euro fine, she pointed out.
The government says it will ban the far-right groups implicated in Méric's death within a month.