The US firm agreed to apply French law and remove offensive messages it is alerted to, said a lawyer for the UEJF union. Such tweets have been proliferating in France in recent days with the hashtag #unbonjuif (#AGoodJew).
The UEJF on Thursday threatened to seek an injunction against Twitter to try to make it remove the offending tweets.
UEJF lawyer Stephane Lilti told AFP that his client had scored an "important victory" over Twitter, which did not immediately react to his statement.
Twitter on Thursday said it had blocked a neo-Nazi group's account at the request of German police.
The move was the first time that the US firm had applied a policy known as "country-withheld content" which allows it to block an account at the request of state authorities.
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