India, Oct. 19 -- It started with a fair complaint: Let's be straight about the beginning. Since September 18, French high-school students have been protesting leaking classrooms, teacher shortages and the rising cost of living. These are real problems, and the state has been slow to fix them. When a teenager lost a hand in Saint-Etienne during the protests, that was a real failure of policing too. Anyone who dismisses the whole movement as a mob is not telling the truth.

But what happened on Saturday was not a protest. About 550,000 people marched peacefully in 110 cities. Then masked groups took over.

In Limoges they burned a police car, broke into the town hall, and set it on fire. The prefect said the roof had collapsed and two-thir...