The Monday figure always tends to dip as there are fewer tests conducted on Sundays.
The seven-day moving average of new infections, which smoothes out reporting irregularities, stood at 8,324, a record for a 28th day in a row, versus a low of 272 on May 27, two weeks after the country ended its two-month long lockdown.
The number of people in France who have died from COVID-19 infections rose by 34 to 30,950. The cumulative number of cases now totals 387,252.