A broad cross-section of turned out across France, including activists from the anti-government Yellow Vest movement and others calling to protect the cultural sector.
"I have two reasons for coming today -- the comprehensive security law and also to support culture," said Kim, a 24-year-old civil service intern.
"Lots of stores are open, the metro is packed, yet cultural sites are closed, even though we can apply protective measures" against the coronavirus, she said.
Also among the protesters were young people calling for the right to hold rave parties such as one in Brittany that attracted 2,400 at the start of the year.
The demonstrators are protesting draft legislation that would ban filming police activities, which the ruling LREM party of President Emmanuel Macron has said it would rewrite.
But people are also protesting the use of surveillance tools such as drones and pedestrian cameras.
Footage of white police beating up an unarmed black music producer in his Paris studio on November 21 has fuelled anger over the legislation, condemned by many as signalling a swing to the right by Macron.
The number of protesters who turned out Saturday was limited by bad weather and Covid-19 restrictions.
#France:-Thousands of people demonstrate at #Paris against the Global Security Law and decrees authorizing the registration of French people according to their political opinions. #MarcheDesLibertéspic.twitter.com/jycrWvpYLS
— Wᵒˡᵛᵉʳᶤᶰᵉ Uᵖᵈᵃᵗᵉˢ𖤐 (@W0lverineupdate) January 30, 2021
France has recorded 75,000 deaths from coronavirus since the outbreak began and the country is bracing for another possible lockdown.
In Paris, the large Place de la Republique was half full, AFP journalists reported, while around 3,000 people had gathered in Montpellier, southern France.
Hundreds turned out for similar rallies in other cities.
The government argues that the proposed law is needed because police officers have become targets of attacks and calls for violence against them on social media.
But French media say a "new national plan of law enforcement" is being used to limit media coverage of demonstrations.
The proposed security law, which has already been approved by the National Assembly, is to be examined by the Senate, France's upper parliamentary chamber, in March.
