Health experts say the actual numbers are likely higher because of a lack of testing, asymptomatic cases and reporting issues.
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French President Emmanuel Macron called on citizens to respect a nightly curfew and other measures to fight the rapid spread of the coronavirus.
Mr Macron says cases are “very strongly accelerating”, with coronavirus patients occupying more than 42% of ICU beds nationally and 64% in the Paris region.
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The government announced a six-week curfew from 9pm to 6am in 46 regions and Polynesia.
France has more than 34,200 deaths, the fourth-highest death toll in Europe behind Britain, Italy and Spain.