French President Emmanuel Macron announced an enforced lockdown, a step similar to curbs imposed by Italy and Spain, saying: "We're in a health war".
Mr Macron also said the European Union's external borders would be closed to travellers from Tuesday.
In Germany, most non-grocery shops and venues have been ordered to shut.
Chancellor Angela Merkel also banned religious services and told people to cancel any domestic or foreign holiday travel. Schools across the country have already been shut.