Only a handful of MPs have raised concerns about the bill, which would allow spy agencies to access phones and emails without seeking permission from a judge.
Among its most contentious elements is its authorisation of so-called "black boxes" on Internet service provider networks that would monitor the data of French citizens for suspicious communications.
That data can then be kept by authorities for five years – or longer if it is encrypted or determined to be suspect.
A handful of French tech companies have threatened to move their operations out of France as a result.
Privacy and human rights experts, meanwhile, have said that the bill should be subject to more debate.
Both the government and main opposition parties support the reform. Officials have pointed to the recent foiling of a terrorist plot on a church near Paris as just the latest cause for concern about the gaps in the country’s intelligence, and Paris has earmarked 425 million euros to recruit spies and investigators to beef up national security and surveillance.
But Clémence Bectarte, a lawyer at the International Federation for Human Rights in Paris, says it is too soon to forget the controversy surrounding the US National Security Agency, or NSA, after its controversial spying programmes were revealed.
“The logic behind this bill is the same as what happened in the States with the Patriot Act, and in the UK, meaning the rhetoric used by the government is that this is to maintain our security when it gravely infringes on our individual freedom,” she told RFI.
The bill also lacks confidentiality guarantees for journalists, lawyers and doctors, which Reporters Without Borders warns could have a chilling affect.
Also among its more controversial proposals is the inclusion of telephone eavesdropping devices that intercept calls by all telephones near a target phone, leading to fears that spies could trawl phone traffic.
“These measures existed before, and were before in the hands of intelligence services in France, but without any legal control,” Bectarte said. “So it’s kind of legalising something that was already existing, but legalising it without any sufficient measures and controls and checks and balances.”