French health chief Jérôme Salomon also said the number of coronavirus patients in intensive care had risen by 359 in the last 24 hours to a total of 4,632.
Some 34 percent of those in intensive care were under the age of 60, Salomon reported.
In total there were 19,354 patients in hospitals across France being treated for coronavirus. Salomon also said 7,132 patients are now known to have fully recovered from the virus.
The death toll of 2,606 is likely to rise given that it only includes those who died in hospitals. A rising number of coronavirus patients are known to have died in care homes for the elderly.
In recent days authorities have been warning that the situation will worsen in the Paris region of Île-de-France, where 823 people have now died.
Health authorities in the region reported another 1,176 confirmed cases on Sunday bringing the total since the epidemic began to over 12,000. However the real number is likely far higher.
There were some 1,694 patients in intensive care in the Paris region on Sunday, a rise of 6.1 percent in 24 hours.
On Sunday March 29th France staged its largest evacuation of coronavirus patients to date from hospitals in the hard-hit east, increasing efforts to free up intensive care units as officials brace for even more serious cases in the coming days.