The capital region of Ile-de-France became the seventh department to announce the move on Wednesday after the COVID-19 incidence rate rose to 446 cases per 100,000 inhabitants.
"The white plan will probably be introduced nationwide in the coming days because it has been adopted in a region after region," Veran told the France 2 television channel.
The measure will mobilize healthcare workers, including by tapping the private sector, and increase the number of emergency care beds available to coronavirus patients. Veran said a person was admitted to ICU every six minutes, down from 10 minutes a week ago.
The minister ruled out new coronavirus restrictions on public life, saying citizens knew what measures protect them from the infection. The French government will instead focus on vaccination and administering booster doses, he added.