All schools and non-essential shops will shut for four weeks, and a curfew will be in place from 19:00 to 06:00.
On Friday, the number of seriously ill Covid patients in intensive care units (ICU) increased by 145 - the biggest jump in five months.
President Emmanuel Macron has promised more hospital beds for Covid patients.
France is currently battling a peak of about 5,000 Covid patients in ICUs. On Friday, the country recorded 46,677 new cases and 304 deaths.
As well as the restrictions that came into force on Saturday, from Tuesday people will also need a valid reason to travel more than 10 km (six miles) from their homes.