Uber Technologies Inc., the car-sharing service that’s rankling cabbies across the U.S., is fighting its biggest protest yet from European drivers who say the smartphone application threatens their livelihoods.

Traffic began snarling in cities including Paris this morning, with a total of more than 30,000 taxi and limo drivers from London to Milan planning blockades in tourist centers and shopping districts. They are asking regulators to apply tougher rules on San Francisco-based Uber, whose software allows customers to order a ride from drivers who don’t need licenses that can cost 200,000 euros ($270,000) apiece.

While similar demonstrations this year have led to smashed windshields and traffic chaos in Paris, a united front in Europe highlights the challenges for Uber’s expansion after a funding round that values the company at $17 billion, almost five times the figure in an earlier…