Left-leaning unions have joined rights groups, including the left-wing Mrap and Socialist-linked SOS Racisme, in calling for demonstrations to "block racism" in all French towns and cities on 30 November.
The ruling Socialist Party is organising a rally in Paris "for the defence of the republic against extremism" three days before, while Culture Minister Aurélie Filipetti is organising an evening of performances "against hatred" at a Paris theatre on 2 December.
Other demonstrations are also being discussed during December as the left rallies round Taubira, who has been compared to a monkey and suffered other racist insults in the last few weeks.
The mainstream right-wing UMP was embarrassed on Friday when one of its local councillors was found to have posted an racially insulting montage based on an old advertisement on her Facebook page.
Party leader announced Saturday that Combs-la-Ville councillor Claudine Declerck would be expelled, although it was later revealed that she had taken the graphic from the Facebook page of a group calling themselves "Loyal Sarkozystes of the UMP".
Taubira has been given three extra bodyguards, making her the most heavily protected minister in the government, a source told the AFP news agency on Saturday.
As the row over the racist invective she has suffered has grown, the minister has received a number of insulting and threatening letters, he said.
While Copé declared in a tweet that "Hatred of others is not acceptable, no matter where it comes from", the far-right Front National (FN) has accused the government of exploiting the question to distract from its political troubles.
"As the FN is in the ascension, they are trying desparately for public opinion to reject it," said former leader Jean-Marie Le Pen, while deputy leader Florian Philippot argued that the best way to end racism is to stop immigration.