The number of infections rose by 16,972 on Saturday, a rise of 5,000 from the previous day, the health ministry said.
It takes the total number of confirmed cases to 606,625. The previous daily record of 16,096 was set last week.
The number of deaths also increased by 49 to 32,198 on Saturday.
There were 4,087 new cases of people being hospitalised over the last seven days, including 849 in intensive care units.
The rate of positive coronavirus tests in France has also risen to 7.9 per cent from 7.7 per cent.
The country has faced two months of increasing infections, which has spread to the country’s elderly and vulnerable populations.
France’s health minister has threatened to close bars and ban family gatherings in Paris as figures showed coronavirus patients have filled about one-third of the intensive care units in the city.
While other countries have imposed local lockdowns, France’s government is taking pains to avoid the mesures and choosing adopting relatively modest localised measures instead.
Health minister Olivier Veran warned that the government could classify Paris and nearby suburbs as a “maximum alert zone” starting on Monday, leading to measures such as shutting bars and banning “family parties” or other big gatherings.
He did not set a limit on group sizes or indicate what the alert zone designation might mean for the French Open, currently under way on Paris’s western edge and open to up to 1,000 spectators per day.
Amid daily protests against virus restrictions on French cafes, Mr Veran said restaurants might be able to stay open if they impose tighter rules.
The maximum alert level means that “the risk of hospital saturation is very high,” Mr Veran said, as authorities unveiled region-by-region data showing that the number of patients in intensive care in some areas is rising faster than the government predicted a month ago.
In Paris, 30 to 35 per cent of ICU beds are now occupied by virus patients, and hospitals delaying some scheduled surgeries to make space for Covid-19 cases, the health minister said.
Paris is now registering nearly 200 positive cases per 100,000 people per week, and more than 100 positive cases per 100,000 elderly people.
Mr Veran said there are signs that the infection growth is slowing in Marseille, Bordeaux and Nice, but said it is too early to lift restrictions, and that France overall is still “in the phase of an aggravation of the situation”.
France has been recording more than 10,000 new confirmed cases a day for the past two weeks, and has reported a total of 31,956 virus-related deaths, among the highest tolls in Europe.