They also estimated there would be just under 2,000 COVID-19 patients in hospital intensive care units in the Paris region around that peak, versus 1,723 as of Thursday.
"The central assumption is for the second wave to peak around April 20, when, in the greater Paris region, we would have slightly less than 2,000 patients in intensive care", he said.
The number of people in intensive care rose by 26 to 2,839 while the total number of patients hospitalised for the disease was down by 52 over 24 hours at 25,567.
Thursday's data were also likely to show that the total number of people vaccinated so far in France was close to 300,000, Veran told a news conference.
One in two intensive care beds are occupied by COVID-19 patients and non-essential procedures are still being postponed to ease the burden on hospitals.
Veran said on Twitter the government had decided to "speed up protection of priority public", meaning medical workers aged over 50 would get a vaccine from Monday.
France has been registering around 15,000 new infections per day, and on Friday confirmed the first case of a new coronavirus variant that recently emerged in Britain.
On Sunday, France registered 11,022 new cases, down from a high of over 86,000 per day a month ago. The number of people in ICUs fell by 10 to 3,220 on Sunday.
During a news conference detailing how France's second national lockdown is about to be gradually unwound, Veran also said the reproduction rate of the disease had fallen to 0.65.