Montpellier is compact and the Écusson is largely pedestrianised, so most of the time you'll walk. For longer hops, the tram is excellent — five lines covering the city and reaching the airport shuttle, the beach tram terminus, and the Odysseum shopping district. Each line has its own playful livery (swallows, flowers, sea creatures); single tickets cost a couple of euros and day passes are good value.
Bicycles are everywhere. The city's Vélomagg' bike-share system has stations across the centre and along the coast. Taxis are plentiful at the station and Place de la Comédie. A driverless extension of tramline 1 to the Mediterranean has been in progress for years — check the current state before counting on it.