The case numbers have risen steeply since the last official figure of 183 cases five days earlier. But there have been no deaths in France attributed to monkeypox.
The normal initial symptoms of monkeypox include a high fever, swollen lymph nodes and a blistery chickenpox-like rash.
Until recently, the viral disease had generally been confined to Western and Central Africa but is now present in several continents, particularly Europe.
Among the latest cases recorded in France, “a first female case has been confirmed, the mode of transmission of which is currently being investigated, and all the others are men,” the French national public health agency said in a statement.
So far, the recent outbreak of monkeypox, which is currently affecting some 40 countries, has mainly affected men who have engaged in gay sex.
The World Health Organization is due to hold an emergency meeting on Thursday to determine whether to classify the global monkeypox outbreak as a public health emergency of international concern.
The virus usually clears up after two or three weeks.
Most of the cases identified in France have been found in Paris and its suburbs, though smaller outbreaks have been seen in several regions throughout the country, including Normandy in the north and the Cote d’Azur in the south.
The first monkeypox case in France was discovered on May 20, the same day the virus was detected in neighbouring Germany.