The tally included 5,889 patients who died in hospital, and 2,189 people in old age homes and other medical facilities, a government statement said.
The daily rise in hospital deaths reported on Sunday was lower than the 441 deaths in French hospitals on reported on Saturday and the record 588 reported on Friday.
The number of coronavirus deaths that have occurred since the start of the epidemic in France's elderly care homes, known as Ehpads, rose slightly after additional reports from Ehpad homes across the country.
The figure stood at 2,189 on Sunday a slight rise on the figure of 2,028 given on Saturday. Not all establishments have reported their figures on residents who have died from coronavirus to the French government, so the number is likely to rise.
Nearly 7,000 patients in intensive care
On Sunday April 5th there were 28,891 patients being treated for coronavirus in French hospitals, a rise of 748 compared to the previous day.
Some 6,948 of these patients were in a serious condition in intensive care.
The one positive note was that the daily rise in the number if people in intensive care in France continued to slow, as has been the trend in recent days.
There were 140 extra patients in intensive care across the country on Sunday, compared to 176 more patients reported on Saturday, 263 on Friday and 382 on Thursday.
France's Director General of Health said in a statement that the figure for those in intensive care was still rising but at a decreasing rate.
“This is the major indicator that allows us to monitor the pressure on hospitals and mobilise all the resources to deal with it, ” read the statement.
In total over 16,000 have left hospital to return home after recovering from the virus.
'The end of confinement is not yet on the cards'
France has been in lockdown since March 17 in a bid to slow the spread of the epidemic, with only essential trips allowed that must be justified with a signed piece of paper.
There have been 70,478 confirmed coronavirus cases in France, but this is not the total as testing for the virus is not universal.
As the country basked in warm sunshine on Sunday and the Easter holiday period started, officials urged people to continue heeding the lockdown rules.
Police checks continued as people around the country were observed flouting restrictions to jog in groups, gather in green spaces and allow children to play together as rural areas received holidaymakers contrary to the government's confinement orders.
“The end of confinement is not yet on the cards, a deadline has not been set,” interior ministry number two Laurent Nunez stressed.
“I remind you of the rule… one goes out only when it is strictly necessary.”
“It's the holidays, the weather is nice, don't give in to the temptation,” urged Valerie Pecresse, president of the larger Paris Ile-de-France region, which is hardest hit by the pandemic.
Forty-one severely ill patients were evacuated Sunday from Ile-de-France's overflowing hospitals and brought to Brittany in the north in two specially-equipped high-speed trains.
In total, more than 550 patients have so far been evacuated from Ile-de-France and the east of France which was the first pandemic hotspot.