PARIS—President Emmanuel Macron is facing unprecedented pressure to roll back his overhauls of the French economy after a fourth consecutive weekend of “yellow vest” protests unleashed another torrent of rioting despite stepped-up security.

The Macron government deployed the full weight of France’s security apparatus on Saturday, but it wasn’t enough to contain a movement that authorities said mobilized 136,000 protesters. They included droves of rioters who waged pitched battles with police in the heart of the French capital...