CGT leader Bernard Thibault called on Mr Sarkozy to recognise the gravity of the situation and "reassess his measures" to deal with the economic crisis.
In Paris, police said some 65,000 demonstrators had joined a march from the Place de la Bastille towards the centre of the city.
There were reports of violent outbreaks on the outskirts of the protest as it reached central Paris, with dozens of youths throwing bottles and lighting fires in a main shopping street.
Police in riot gear charged the youths, pushing them back on to the Place de l'Opera where the crowds were gathering, but the situation remained volatile.
There were repeated baton charges, and after fires were lit on some of Paris' best-known boulevards, police used tear gas on the minority of protesters who were violent.
Earlier, some 25,000 to 30,000 people rallied in the city of Lyon, according to organisers and police.
In Marseille, organisers and the authorities disagreed, with the former putting the number of demonstrators at 300,000 but the police estimating 24,000 had taken part.
The protests are against the worsening economic climate in France and at what people believe to be the government's poor handling of the crisis.
Opposition Socialist Party leader Martine Aubry said people were out in the streets "to express what worries them: the fact that they work and yet cannot make ends meet, retired people who just can't make it [financially], the fear of redundancies, and a president of the Republic and a government that just don't want to change policy".
The strike action disrupted transport services but did not cause the paralysis forecast by unions.
Regional trains and those in and around Paris were hit, and a third of flights from Orly airport were cancelled.
Striking is... the national sport, a selfish and narrow-minded way of dealing with just about any disagreement
Forty per cent of regional services were running, train operator SNCF said, and 60% of high-speed TGV services. Three-quarters of metro trains were running in Paris.
Paris's second airport was heavily hit by the strike, but flights out of the larger Charles de Gaulle hub were experiencing only short delays, AFP news agency said.
Schools, banks, hospitals, post offices and courts were also hit as workers stayed at home. Officials said just over a third of teachers and a quarter of postal and power company workers were on strike.
According to a 25 January poll by CSA-Opinion for Le Parisien, 69% of the French public backs the strike.
"I'm tired and frozen after waiting half-an-hour on the platform," commuter Sandrine Dermont told AFP as she arrived by train in Paris.
"But I'm prepared to accept that when it's a movement to defend our spending power and jobs. I'll join the street protests during my lunch break," she said.
Many people are furious that Mr Sarkozy said there was no money left to raise wages and consumer spending power, but nonetheless managed to find billions of euros to bail out floundering French banks, says the BBC's Emma-Jane Kirby in Paris.
The walk-out has affected transport, education and postal services throughout the country, our correspondent says, and is the biggest one-day strike since Mr Sarkozy took up office.
Commuters at St Lazare station in Paris
With unemployment looking likely to reach 10% next year, she says, the protesters hope he will drop his programme of cost-cutting reforms and focus instead on protecting workers' jobs and wages.
Mr Sarkozy cannot ignore this demonstration of anger, our correspondent adds. Street protests have repeatedly brought down French leaders and Mr Sarkozy does not want his government added to that list of casualties.
"We want to show how the people are dissatisfied with the situation at the moment," Thierry Dedieu of the CFDT general workers' union told the BBC.
People had the feeling they were paying for a crisis they were not responsible for, he added.
But earlier in the week, French Finance Minister Eric Woerth condemned the strike organisers, accusing them of scare-mongering during a time of economic uncertainty.
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