Paris revealed yesterday it will pay 84 per cent of the wages of one parent in each household with a child under the age of 16 if their school is forced to close down due to the virus.
French health authorities on Saturday reported 10,561 new confirmed Covid-19 cases in the past 24 hours, a new daily record as the number topped 10,000 for the first time.
Local lockdowns can not be ruled out in French regions where COVID-19 infections are flaring up even though authorities are striving to avoid it, a government advisor said on Thursday.
That figure has now shot up for 12 days in a row.
In a recent interview, French Health Minister Olivier Veran said hospitalization and the number of serious cases were "the reflection of the epidemic situation of two weeks ago", expecting both indicators to worsen further in the next 15 days.
Castex, speaking after a meeting of France's most senior officials to discuss the epidemic, said the rise in cases was particularly worrying in three areas - the cities of Marseille and Bordeaux, and the French Caribbean territory of Guadeloupe.
In March, France had imposed a strict lockdown.
Government spokesman Gabriel Attal said earlier yesterday that nothing would be ruled out at Friday's cabinet meeting, while President Emmanuel Macron said he hoped any new measures would not be too restrictive.
"We need to be as transparent and clear as possible", Macron said Thursday.
The number of COVID-19 deaths also climbed by 40 over the last 24 hours, to reach a total of 30,893 casualties.
France is seeing an acceleration of the Covid-19 outbreak after a surge in infections but aims to avoid any new nationwide lockdown, Prime Minister Jean Castex said Friday.