You have two options at the airport, a taxi or the airport bus. The bus is timed to meet incoming flights. Timetable : https:/…210-aeroport-04-06-2018.pdf and the bus fare is €1,60 taxi obviously a lot more than that.
Montpellier's main railway station is St Roch, in the city centre. If you did take one of the few trains that calls at the new Sud station you would be miles out.
One end of the St Martin area is no more than 250 yards from St Roch, but the other end is four stops on the tram, so completing the trip the 'best' way could be a short walk. Depends then which street.Edited: 11:21 am, July 26, 2018