The bill notably aims to ban individuals identified as habitual hooligans from taking part in demonstrations, and force protesters involved in acts of violence to pay for the damage.
Some MPs also want more severe penalties for organisers of unauthorised demonstrations as well as people who cover their faces during violent protests.
But the bill has drawn fire — even within President Emmanuel Macron's own centrist party — from critics who say the proposals represent a threat to civil liberties.
Announcing the draft law earlier this month, Prime Minister Edouard Philippe said some of the anti-Macron “yellow vest” protests had led to unacceptable violence.
“In many towns in France, demonstrations have been peaceful — but we cannot accept some people taking advantage of these demonstrations to cross the line, break things and set things on fire.”
Freedom to protest
The protests began in November against rising fuel taxes, but quickly spiralled into a wider revolt over accusations that Macron, a former banker, is out of touch with ordinary people in small-town and rural France.
Across France tens of thousands have joined protests and road blocks, although the numbers have eased in recent weeks after Macron announced a series of policy climbdowns and a public consultation so people could vent their anger.
In several cities — but especially Paris — the weekend protests have repeatedly descended into violence.
Rioters in the capital torched cars and looted shops in early December, and also ransacked the Arc de Triomphe monument.
Interior Minister Christophe Castaner insisted the bill, backed by police unions, was not “an anti-yellow vest law” or “anti demonstration” law.
“It's a law to protect demonstrators, shopkeepers, local residents and police,” he told BFM television.
Yael Braun-Pivet, the LREM head of the national assembly's cross-party laws commission, said protecting the right to demonstrate would be front and centre in the debate.
“What guarantees are being put around this procedure?” she demanded, telling the Journal du Dimanche newspaper earlier this month that she was “reticent” over certain measures.
Leftist critics have decried the bill as “liberticide” and have been little reassured by Castaner's suggestion that a protest ban would concern fewer than 300 people.
Already revised by Braun-Pivet's commission, more than 200 amendments have been proposed to the bill, with a final vote due next Tuesday.
The draft law could also see protesters who mask their faces fined up to 15,000 euros ($17,000) and handed a one-year prison term.