These included a policewoman being repeatedly kicked and beaten in a “savage” assault that was filmed and posted on social media (see video below) in the southeastern Paris suburb of Champigny-sur-Marne.
“It's not normal for police to be beaten up like that,” said Alain, 55, in front of the police station in Champigny, where about 100 police gathered at the Alliance union's call.
Police also protested in Lille, Saint-Etienne, Grenoble, Toulouse, Carcassonne, and Bordeaux.
And on Tuesday evening around 70 people gathered at the Trocadero in Paris responding to a call from the association, “Angry Female Police Officers”.
“We want to challenge policies on the growing evil of hatred for police officers,” Perrine Sallé, spokesperson for the association told AFP.
Some French politicians have voiced their support for the country's police force.
“Violence and a lack of respect for the authority of the state have become commonplace,” said Bruno Retailleau from the right wing Les Republicains party.
Figures show that half of the 4,079 gendarmes injured during interventions in 2016 were assaulted and the number of police injuries caused by weapons was up 60 percent, according to Le Parisien.
President Emmanuel Macron called the crime against the female police officer a “cowardly and criminal lynching”, and vowed that those responsible would be caught and punished.
On Tuesday, reports of another attack on police officers emerged, this time in the northern suburb of Aulnay-sous-Bois when police stopped two youths suspected of stealing a scooter.
One officer was punched several times while another fired his gun into the air to scare off the attackers.
The attacks on the police were widely condemned by France's outraged political class, who offered solidarity to the injured officers but also demanded swift and tough justice for those responsible. Far right leader Marine Le Pen demanded a reform to allow police to greater use of “legitimate defense” to respond to such attacks.
Pressure grew on France's interior minister Gerard Collomb, who called the attacks “savage” and “unacceptable”.
He denounced a “society of violence” that “cannot continue to exist”.
History of violence
But the two New Year's attacks on police are just the latest in a long line of incidents in which the forces of law and order have been targeted.
French police have long suffered testy relations with youths in poor immigrant-heavy suburbs, not least since the nationwide riots in 2005 sparked by the death of two teenagers who were electrocuted while hiding from officers.
The assault of a young man by police in Aulnay-sous-Bois — which led to officers being charged, including for rape after a truncheon was shoved up the youth's anus — sparked fresh unrest last year.