French Prime Minister Jean Castex promised on Saturday that the government would "go all out on vaccinations" and would not immediately end government aid for the restaurant sector once they can reopen.
"We have one month, a month and a half to two very sensitive months," Castex told a restaurant owner amid his visit to the centre of the country.
The more transmissible variant of COVID-19 that was first detected in the UK rapidly has become the main strain of the virus in France over the past few weeks.
"This variant risks driving us back, I'm not sure, possibly to lockdown," Castex said, emphasising that it meant speeding up the rollout of coronavirus vaccines in March and April.
France locked down in late October of last year and has had a nightly curfew since emerging from its second lockdown. That curfew was later extended from 6:00 pm to 6:00 am.
It has kept new COVID-19 cases at a plateau but with the more transmissible variants, infections have been increasing.
The government has begun implementing local weekend lockdowns in areas where the virus is spreading more rapidly including in Dunkirk and Nice.
Castex said amid a visit to Creuse on Saturday that the government would continue to try to help the restaurant sector, stating that it was "the most heavily and the longest impacted by the crisis."
But when asked about people who work in theatre, who have protested for more support from the government, Castex invited them to "to go for a walk in Germany, in Italy to see how much they are compensated."
The French government has been heavily criticised along with the European Union for the slow rollout of its vaccination campaign.
Officials said earlier in the week that just 30% of healthcare workers had received a COVID-19 vaccine, encouraging people to get vaccinated.