Under the proposed law, which would also have to pass in the National Assembly, protesters could be required to pay up to €10,000 for damage caused during demonstrations.
About 70,000 law enforcement officers were mobilised ahead of Saturday's planned protests after authorities bolstered security following last weekend's riots.
As France readies itself for another day of nationwide protests, the government's efforts to prevent renewed violence have prompted criticism from some.
A massive security operation has been deployed across France for major protests on Saturday. Businesses across the country remain tense following violence which overshadowed peaceful demonstrations last weekend.
Some military forces from Operation Sentinelle will be deployed to free up police and gendarmes for the expected demonstrations, French Interior Minister Laurent Nuñez said.