Todd, a historian, anthropologist and sociologist whose political sympathies are firmly on the left, caused a storm this month with the publication of Qui est Charlie? (Who is Charlie?).
The majority of the estimated four million demonstators were middle class and white, Todd claims.
While they may have believed they were defending freedom of expression and secularism, their "latent values" were the expression of "social power" and "domination" and their "most important need was to spit on the religion of the weak".
At the time "no critical analysis could have been heard", Todd says.
He also lays into Valls's Socialist Party, accusing it of selling out to the dictates of the eurozone and being "subjectively" anti-racist but "objectively xenophobic" because "it excludes the children of immigrants from the French nation".
In a virtually unheard-of move for a French prime minister, Valls then took to the columns of Le Monde newspaper to return fire.
Todd himself is guilty of "imposture", he argued, and expresses an "ambient cynicism" championed by "intellectuals who no longer believe in France".
The 11 January demonstration was "in no way" Islamophobe, Valls argues, and cartoons of Mohammed "are on the side of those suffering the weight of fundamentalisms and the violence of fanatics who destroy, terrorise and murder".
The idea that the country is run by a globalist elite that betrays the people feeds populism and extremism, the prime minister claimed, accusing Todd of believing in the "revolutionary myth" that the left only exists to protest and calling for the "standard of optimism to be raised".
None of which pleased Todd, who hit back on Friday by comparing Valls's intervention in the country's intellectual debates to the cultural policies of the wartime collaboration government of Marshal Philippe Pétain.
"Either Manuel Valls hasn't read my book or he's completely stupid," he told RMC-BFM radio. "Unemployment is 10 per cent ... Islamophobia is spreading ... anti-Semitism is spreading ... Manuel Valls's optimism is the optimism of the national revolution and of Marshal Pétain."
The left-wing intellectual received support from a quarter he may not welcome on Thursday.
Front National vice-president Florian Philippot slammed Valls's intervention as part of a "general offensive against freedom of expression", comparing it to the outcry against far-right media pundit Eric Zemmour and atheist philosopher Michel Onfray, who has become increasingly critical if Islam.