The protesters beat one officer, who died on Tuesday, and wounded at least 40, a police spokesman in eastern Lahore told Reuters.
Samuel Paty's alleged showing of the caricature is suspected to have led to his murder.
"It has been said that his wife is 20 years older than him, and that she is a relative of Rothschild, the richest Jew."
Some 12 million pupils returned to school for the first time since the 47-year-old was slain in broad daylight on the eve of a two-week school holiday.
"The Muslim world will not tolerate such blatant disrespect of the Prophet Muhammad (PBUH) and stands in solidarity with their French Muslim brothers and sisters," the council said.
Three protesters were reportedly arrested after clashing with police forces.
The video included a song uploaded by far-right fans of one of Israel's largest Premier League soccer clubs - Beitar Jerusalem.