Under the rules, the unvaccinated will no longer have access to places such as restaurants, cinemas or long-distance trains.
Early on Thursday morning, the National Assembly approved the bill in its first reading. Now the Senate has to deal with the text.
The National Assembly had previously interrupted the deliberations twice, thus jeopardizing the government’s tight schedule.
In view of the rising number of coronavirus infections, the government wants to replace the so-called health pass, which until now has provided proof of vaccination, a current negative coronavirus test or recovery from an illness, with a new vaccination pass. A negative test will then no longer be sufficient.
The government plans to decide at a later date what status those who have recovered will receive. The rules were supposed to come into force on January 15.
Whether this timetable can be kept is unclear in view of the delayed approval in the National Assembly.
Infection figures have been rising sharply in France in recent weeks.
The Omicron variant is now predominant. On Wednesday, the country recorded a peak of more than 332,000 reported infections within one day.
Most recently, the incidence rate – the number of new infections within a week per 100,000 people – was around 1,908 nationwide.