Dunkirk is a shrinking, suburban city on the northern coast of France. It’s a car town, where public buses are a mode of last resort: They represent only five percent of trips.

But when Patrice Vergriete ran for mayor in 2014, he envisioned something different: a sustainable city that allures and serves young people, families, and the elderly alike. So he made a radical campaign promise, which he thinks helped him win: make the buses free.

“I wanted to give back purchasing power to the families,” …