PARIS—A spate of anti-Semitic incidents has accompanied France’s yellow-vest protests in recent weeks, raising fears that the movement is stirring up hatred in the nation that is home to Europe’s largest Jewish population.

On Saturday, protesters clad in reflective yellow vests were filmed accosting Alain Finkielkraut, a prominent public intellectual, as he walked with his mother-in-law on the street in Paris, calling him a “dirty Zionist s—” and other insults. A video of the incident went viral online, prompting condemnation...