France had on April 6 recorded 605 deaths in hospitals, its highest daily number so far.
For the fourth consecutive day in a row, the number of patients in intensive care fell with 35 fewer patients, making a total of 6,845 people needing such treatment.
The health ministry reaffirmed that a "plateau" appeared to have been reached but warned the situation remained serious despite the slightly improving data.
"We must stay vigilant as the hospital and intensive care services are taking in very many patients," it said.
France has been in lockdown since March 17 in a bid to slow the spread of the epidemic, with only essential trips allowed.
French President Emmanuel Macron is due on Monday to address the nation for a third time during the crisis and is expected to announce that the lockdown will be extended beyond its current April 15 expiration date.
Macron will have to steer a careful course amid the tentative signs of improvement, telling people they must still stay at home while giving indications about how the confinement measures might be relaxed.
