In Paris, protesters paraded through the city centre behind a banner condemning "state crimes". Other demonstrators carried "Black Lives Matter" banners, AFP reported.
Several people spoke at the rally to tell the stories of members of their families who had died at the hands of the police.
Interior ministry figures put the turnout out at 2,100, but the march organizers estimated 8,000-10,000.
The interior ministry said another 11 protests took place elsewhere in France, saying the total turnout for these protests was 1,400.
Other protests took place in Bordeaux and Toulouse in the south-west, and Lyon in the south-east.
Saturday's demonstration comes two days ahead of International Day for the Elimination of Racism.
It is held on March 21 to mark the day, in 1960, that police in apartheid South Africa opened fire on a peaceful demonstration, killing 69 people.