Thousands of anti-Semitic jokes were posted last week using the Twitter hashtag #unbonjuif, meaning "a good Jew," France 24 reported Wednesday.
By Oct. 10, the hashtag was trending third in France and a deluge of offensive posts continued for days.
SOS Racisme and the French Jewish Students Union both said they are determined to pursue those who took part in the courts.
Director Guillaume Ayune of SOS Rasime said lawyers are currently exploring "all avenues for legal action."
"We absolutely have to tell people that just because they are sitting behind a computer, they can't assume they'll get away with making racist comments."
President Jonathan Hayoun of the French Jewish Students Union said his organization will file a complaint at a Paris court demanding Twitter remove references to the "a good Jew" hashtag, provide IP addresses of offenders and delete the offensive tweets.