In Bordeaux, three women walked through the streets topless with slogans in support for the strikes emblazoned on their skin.
It is the third time that labour unions have sought to stage a nationwide show of strength since President Emmanuel Macron began his five-year term in May 2017.
Images showed riot police charging at protesters with batons in Paris, firing stun grenades and tear gas.
Some protesters destroyed two shops and a bus stop.
Police said 20 demonstrators were arrested.
Tuesday's strikes came from all of the large labour unions and involved organisation of street rallies in about 140 cities, towns and villages across France.
Postal workers, air traffic controllers, state teachers and public administration workers were urged to quit their posts yesterday.
They joined marches to denounce what the unions say is an erosion of spending power and the public service itself under Macron.
One catalyst for union anger is a proposal to end certain sick leave perks and cut 120,000 government administration posts.
Also on the cards is an increased recourse to contract hiring rather than the job-for-life recruitment that is standard in the French civil service.
In all, France has about 5.7 million employees in government administration, state agencies, schools and hospitals.
"We're demonstrating in defence of a public service that is there to serve everyone, wherever in the country they live," Philippe Martinez, head of the Communist-linked CGT union, told RTL radio.
Daily Star
More about: France
