PARIS, Nov 22 (Reuters) - French Prime Minister Jean Castex has tested positive for the coronavirus and is isolating himself, the prime minister"s office said on Monday. Castex, who is fully vaccinated against the virus, learned his daughter had tested positive after he returned from Belgium, where he met his Belgian counterpart Alexander De Croo. Castex then tested positive himself. The French prime minister will continue to work and will remain in isolation for 10 days, his office added in a statement. Castex"s positive test coincides with several European countries tightening restrictions to slow down infections and the number of people being hospitalized with COVID-19. Austria on Monday re-imposed a nationwide lockdown. read more French President Emmanuel Macron has said France doesn"t need to follow such measures because its stringent health pass rules have helped keep the virus in check, but he wants to accelerate the delivery of vaccine booster shots. Last week, France"s health regulator recommended booster shots for over 40s. Currently it is available to over 65s.