Police reported a number of clashes on the sidelines of protests in the capital Paris after demonstrators gathered in front of the French Health Ministry.
A number of rubbish bins had been set on fire, police said on Twitter. The police called for calm, adding that they had made 16 arrests.
More than 220 protests were announced nationwide, the news platform France info reported, after unions and collectives called for a national day of action.
Health workers are demanding better pay and a less profit-oriented focus for hospitals.
Demonstrations were also held in front of clinics in the southern cities of Montpellier and Marseille, and in the north-eastern city of Metz.
Medical staff also took to the streets in the Alsatian cities of Strasbourg, Colmar and Mulhouse, according to reports in the Dernieres Nouvelles d’Alsace newspaper.
The French health system was pushed to its limits during the coronavirus pandemic, particularly in the badly-hit Grand Est region.
Prime Minister Edouard Philippe previously promised salary increases for hospital staff, and his government has tabled further health-care reforms.
The pandemic has so far claimed more than 29,000 lives in France. President Emmanuel Macron on Sunday announced a further easing of the country's lockdown, pledging life could begin to return to normal.
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