The rise led the government to outline additional measures on Friday to avert a return to the general lockdown put in place earlier in the year.
The latest daily count of 10,561 new infections, surpassing the previous record of 9,843 new infections reported on Thursday, highlights a resurgence of the disease in France.
The 10,561 new cases on Saturday breaks a record of 9,843 Covid-19 infections set just two days previously as countries across Europe battle to prevent getting a second wave
France has reported more than 10,000 infections of coronavirus in a single day for the first time.
Mr Castex, who came out of self-isolation on Saturday after coming into contact with someone infected with the virus, said the pandemic in France is “obviously worsening”.
Prime Minister Jean Castex promised steps to speed up tests and toughen local measures in high-infection zones.
In its daily update, the French health ministry also reported that 772 clusters were being investigated, an increase of 86 in the past 24 hours.
It was reported last month that coronavirus cases in France were accelerating at an “exponential” rate as the country fought to try and prevent a second lockdown.
The death toll since the start of the Covid-19 outbreak this year in French hospitals and nursing homes has reached 30,910, with 17 deaths recorded in the past 24 hours, it added.
Over the past week, there had been 2,432 arrivals in hospital for Covid-19, including 417 entries into intensive care units, the ministry said.
The rises led to fears the country may be about to experience a second wave of the deadly disease, which has so far claimed the lives of more than 30,000 people.