A hearing is set for January 8 at a Paris court, attorney Stephane Lilti said, adding that the group was also seeking the implementation of French laws on illicit content.
The lawyer representing Twitter was unavailable for comment.
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.