The ruling follows a legal complaint lodged in October by France's Union of Jewish Students (UEJF) which argued that numerous tweets had breached French law prohibiting incitement to racial hatred.
The union took the legal action against Twitter to force the site to reveal details on people who posted a slew of anti-Semitic hate messages.
The court in Paris on Thursday said Twitter must now do this "within the framework of its French site".
Speaking to The Local after the court's decision the president of the UEJF Jonathan Hayoun said the ruling was important step in the fight against anti-Semitism.
"Anti-Semitic abuse is just the same whether it's out on the street or on Twitter. The court has made it very clear that Twitter needs to help the police in identifying those who post hateful messages.The authorities must now do their job.
" This is not an attack on freedom of speech at all. We are living in a climate of anti-Semitism in France."
In October, the UEJF said it had forced Twitter to take down many offending tweets that had flooded the site under the hashtag #unbonjuif (#agoodjew), with examples including: "#agoodjew is a dead Jew".
Following that, more anti-Semitic messages were sighted with a new keyword, #unjuifmort (#adeadjew).
A Twitter spokesman refused at the time to comment directly on the tweets and reiterated the company's standard response that it "does not mediate content".
He added: "If we are alerted to content that may be in violation of our terms of service, we will investigate each report and respond according to the policies and procedures outlined in our support pages."
These state that Twitter cannot delete tweets but allow for accounts generating content in breach of its rules or considered illegal to be suspended.
The site had also said it would not hand over details of account holders unless ordered to do so by a judge.