PARIS—Days after taxi drivers burned tires and snarled traffic across France in late June to protest Uber Technologies Inc., two lobbyists for the car-hailing firm walked into the offices of France’s top cop.

Mark MacGann, Uber’s public-policy chief in Europe, said the company was willing to suspend its popular, low-cost Uberpop service, which relies on nonprofessional drivers. But he said the French government also should loosen rules on how to become a licensed driver for Uber’s other services.

French...