Police say around 2,500 mostly demonstrators gathered at place de la République, some waving placards bearing the '#Metoo' hashtag.
CGT union boss said authorities' U-turn on march was a 'victory for democracy' and urged workers to turn out in 'massive' numbers on Thursday.
A Polish national with a record of violent crime has confessed to abducting and strangling the nine-year-old on April 15th.
The Paris march was against a bill of law by which doctors consultation fees are paid in arrears by health fund, instead of upfront by patients.
Meeting follows Sunday's massive marches but also comes amid questions over how militants known to authorities were able to launch deadly raids.
The emotional march, which is expected to attract more than a million people, will be led by relatives of the victims of last week's attacks.
Temperatures in the French capital reached 21.6 degrees Celsius, beating the 1880 record of 20.7 degrees Celsius, according to Meteo France.
The march, mirrored by smaller protests nationwide, follows recent racist outrages, including crude attacks on France's black justice minister.
The number of registered job seekers in March rose to more than 3.224 million, the worst level since records began in January 1996.
With just two weeks to go before the first round of the French presidential elections, growing anger over the uncertain fate of one of the last major steel-making plants in France has returned the issues of de-industrialization, globalization and the social responsibility of corporations to the fore of the political agenda. Exhausted but triumphant, a group of workers from the ArcelorMittal steel mill in Florange, north-east France, finally reached Paris on Friday amid public cheers and a battery of TV cameras after a marathon ten-day, 330-kilometre march in protest at the feared closure of part of their plant. Mathieu Magnaudeix was there to follow the men, now known across France as ‘the ArcelorMittals’, who have become the heroes of a decimated industrial heartland.