Demonstrations in Paris and other cities over plan for mandatory vaccinations for health workers and vaccine pass for public places.
Some demonstrators waved Russian flags and held banners calling for greater cooperation between Mali and Russia.
Protestors are unhappy over recent rejection by French constitutional court of parts of a law intended to protect regional languages.
The decision not to try Kobili Traoré over 2017 killing of Sarah Halimi, 65, has provoked international outrage.
Demonstrators, including gilet jaunes or 'yellow vest' activists, also protested against Covid restrictions.
Proposed legislation to ban the dissemination on social or traditional media of police officers' faces, justified as protecting the safety of police staff, and which would apply to civilians and journalists alike, has prompted street protests in Paris and other cities across the country over what demonstraors say is a law which would gag disclosure of police abuses.
There were more fierce protests and calls for a boycott of French goods in Muslim countries on Monday following President Emmanuel Macron's defence of the right to publish cartoons of the prophet Muhammad during a homage to teacher Samuel Paty who was beheaded by a fundamentalist for showing the cartoons to his pupils in a lesson on civic rights and free speech.
Meanwhile the number of new COVID-19 cases in France rose by 10,561 on Saturday - the highest daily number since the pandemic began.
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.
A procession of around 15,000 people, according to official estimates, marched through central Paris on Saturday, along with several thousand in other cities and towns across France, protesting racism and police violence in the country and highliting the case of a black man who died in strikingly similar circumstances to Afro-American George Floyd in Minneapolis last month.
French interior minister Christophe Castaner said the case of Gabriel Djordjevic, 14, who sustained a fracture to his eye socket and four broken teeth after he claimed he was kicked by a police officer, was 'troubling'.
Protests around France continued on Thursday over alleged racist violence by police, prompted by a campaign by the family of Adama Traoré, a 24-year-old man of Malian origin, for a full investigation into his death in police custody allegedly from asphyxiation, and the outrage over the death in the US of George Floyd, 46, an Afro-American who was suffocated by a police officer during his arrest in Minneapolis.
Algeria singled out two documentaries broadcast on Tuesday by France 5 and the former colonial power's Parliamentary Channel, about the recent protests.
In Lebanon, the lockdown to contain the coronavirus pandemic came as the final blow to the Middle East nation’s collapsed economy which has left half of the population living in poverty. Mass anti-government demonstrations which erupted last autumn have now flared up again amid food shortages and galloping inflation. Their anger has now turned on Lebanon’s banks for having acted as the burning fuse for the financial meltdown. Justine Babin and Nada Maucourant Atallah report from the capital Beirut.