The ruling comes after appeals from Twitter failed in France to protect the identities of the people behind the Tweets.
The High Court in Paris told Twitter in January that they would have to give the names of the people who posted anti-Semitic posts to the french Union of Jewish Students and four other groups if they were requested to.
Twitter had already blocked the posts in France but had appealed against handing over the identities of those behind the Tweets following a complaint from the French Union of Jewish Students.
While the court has ruled that the names of the people must be handed over it is being reported that Twitter may well be considering appealing again against the ruling.
A spokesperson for Twitter said: “We are disappointed that the court has decided not to hear our appeal. We are considering our options, including resubmitting the appeal.”
According to the court in Paris Twitter had not come up with a convincing reason as to why the identities of the people behind the racist tweets should be protected. The court added that Twitter had also not set up an “easily accessible and visible” way for people to be able to let the site know about content that constituted crimes against humanity and incitement to racial hatred.
This case has been running since October 2012 when the french Union of Jewish Students asked Twitter to delete posts with the hashtag #unbonjuif (#agoodjew#). The group claimed that the posts were in breach of French laws regarding racial hatred.
The posts in question were hidden from users in France to comply with the law but the members of the students union and four other groups want to have the identities of those who posted the Tweets revealed so they can then be prosecuted.
In March the French Union of Jewish Students also filed a $50 million law suit against Twitter claiming that the company had failed to respect the time frame imposed by the court to reveal names – this has been appealed by Twitter.
A spokesman from the French Union of Jewish Students said that twitter was “playing with the French legal system”.
He added: “Twitter has not made any progress in regards to respecting our country’s laws.
“The first step towards making any kind of progress could be finally listening to the court’s decision, and making sure that its social network is not a lawless place.”