PARIS—Thousands of people today gathered in metropolitan areas across France on Saturday to protest law enforcement brutality and systemic racism, amplifying appeals that have reverberated all around the globe due to the fact the killing of George Floyd in Minneapolis.

Organizers hoped to create on the momentum of previous protests and to drive for an overhaul of law enforcement tactics that protesters say have exacerbated tensions in between French law enforcement and minorities who populate the country’s blighted banlieues. Demonstrators have drawn a parallel in between Mr. Floyd, a black…