French lawmakers on Tuesday widely approved a bill that cracks down on illegal drug trafficking by empowering prosecutors, toughening the penalties for traffickers and giving the police more investigative tools.

The move, which paves the way for the measures to become law, was a rare case of successful policymaking in France’s lower house of Parliament, the National Assembly. Lawmakers there have been hobbled by political fractures, but they have joined to express growing concern over the far-reaching impact of crime and violence tied to the drug trade.

The National Assembly approved the bill with 396 votes in favor and 68 against. Its passage was a win for the government of Prime Minister François Bayrou, who survived a no-confidence motion in February to pass a budget but who is still at the mercy of the divided lower house.

“Everyone knows the current political difficulties: no majority in the National Assembly, a complicated path for major bills,” Bruno Retailleau, France’s interior minister, a conservative who championed the bill, told lawmakers on Tuesday.

Mr. Retailleau said that the broad support for the bill showed that lawmakers understood that drug trafficking and organized crime were “often the root cause of hyper-violence” in France and an “existential threat” against its institutions.

Some left-wing lawmakers expressed concern about the focus on cracking down against drug traffickers, rather than the root causes of their trade, but only the hard-left France Unbowed party ultimately voted against the bill. Green lawmakers and a handful of others abstained.