The French Jewish Students Union (UEJF), SOS Racisme and SOS Homophobie say they found 586 offensive posts between 31 March and 10 May.
But they claim only a small percentage was taken down.
French law states that racist, homophobic and anti-Semitic content must be removed from websites.
“In light of YouTube, Twitter and Facebook’s profits and how little taxes they pay, their refusal to invest in the fight against hate is unacceptable,” said UEJF president Sacha Reingewirtz.
The three social networks have all been contacted by the BBC.
YouTube’s community policy states that the platform does not support content which “promotes or condones violence against individuals or groups based on race or ethnic origin, religion, disability, gender, age, nationality, veteran status or sexual orientation/gender identity, or whose primary purpose is inciting hatred on the basis of these core characteristics”.
Facebook has a similar guideline but adds that it does allow “clear attempts at humour or satire that might otherwise be considered a possible threat or attack”.
Twitter’s rules state: “We believe in freedom of expression and in speaking truth to power, but that means little as an underlying philosophy if voices are silenced because people are afraid to speak up.” For that reason, it continues, it does not tolerate behaviour that “crosses the line into abuse”.