Almost 3,800 Covid-19 infections were confirmed in the past 24 hours, the health ministry's DGS public health division said.
“All indicators continue to climb and transmission of the virus is intensifying,” the DGS said in a statement.
More than 3,000 new daily cases have been registered on just two days since May, on Saturday and Sunday last weekend.
Several departments in both the Île-de-France region around Paris and the Provence-Alpes-Côte d'Azur region around the Mediterranean port city of Marseille on Wednesday passed the “alert threshold” of 50 new daily cases per 100,000 inhabitants, the DGS said.
Nationwide, more than 16,700 infections have been detected over the past week.
Meanwhile the number of people in intensive care because of the virus remains comparatively low at 374 and the death rate has not seen a spike.
Since the coronavirus emerged late last year, more than 225,000 people have been infected in France and almost 30,500 have died.