The Mémoires et Partages (Memory and Sharing) organisation, based in Bordeaux and Dakar, on Monday called on the government to stop the cancellation of the show, which was ordered by Bordeaux's Socialist mayor, Samuel Hazard, on Friday after what he described as a deluge of hate during the week.
"It's still possible to review this cancellation because even the good God's pencil has a rubber," the NGO wrote in a statement, quoting French West Indian poet and politician Aimé Césaire.
And it called on the government to "use all its powers to defend the unity of French youth in its diversity ... and the right to participation and citizenship of all its children's, even if they have strayed".
A far-right website last week quoted lyrics from numbers by Black M's previous group, Sexion d'Assaut, that it claimed showed that he was "anti-France", homophobic and anti-Semitic.
MPs and local councillors from the far-right National Front and from the hardline wing of the mainstream right Republicans joined the clamour and called for the performance to be scrapped.
Hazard says he was inundated with emails and phone-calls, many of them overtly racist.
Socialist politicians later responded by accusing the right of being "thought police" and other rappers claimed that Black M was being targeted because of his race, not his music.
"This expulsion, a veritable capitulation of the state to extremist and Frontist hate is an institutionalised massacre of national solidarity," commented Mémoires et Partages president Sira Diallo.The organisation was given an award for an exhibition on soldiers from French colonies and from ethnic minorities in the French army.
Education Minister Thierry Mandon on Sunday condemned the "indecent" attacks by the National Front on Black M and Republicans MP Benoist Apparu on Monday called for the concert to go ahead, accusing the government of "capitulation".
But another MP from the same party, Hervé Mariton, repeated the accusations against the rapper, declaring "Talent is not an excuse for everything".