The "ecocide" proposal topped dozens of ideas presented by the 150 randomly picked members of the Citizen's Convention on Climate, along with inscribing the fight against global warming in the French Constitution.
Protesters marched through Paris with signs reading "Laissez nous respirer" ("Let us breathe") in reference to George Floyd, and protests also took place in the UK.
Claims have emerged that prosecutors were pressured to move fast in a fraud inquiry against former prime minister François Fillon, his main right-wing rival in France's 2017 presidential race.
Casinos will welcome gamblers from Monday while stadiums and racetracks will reopen on July 11, subject to a limit of 5,000 people, the government announced late on Friday.
The Constitutional Council said the measure put the onus for analyzing content solely on tech platforms without the involvement of a judge, within a very short time frame, and with the threat of hefty penalties.
The city in east France has been rocked by clashes and vehicle burnings after an assault this month on a 16-year-old Chechen boy that prompted other members of the community to stage reprisal raids.