We present the integrated Halpha emission line profile for 157 HII regions in the central 3.4' x 3.4' of the galaxy M 83 (NGC 5236). Using the Fabry-Perot interferometer GHaFaS, on the 4.2 m William Herschel on La Palma, we show the importance of a good characterization of the instrumental response function for the study of line profile shapes. The luminosity-velocity dispersion relation is also studied, and in the log(L)-log(sigma) plane we do not find a linear relation, but an upper envelope with equation log(L)=0.9*log(sigma)+37.6. For the adopted distance of 4.5 Mpc, the upper envelope appears at the luminosity L=10^38.5 ergs, in full agreement with previous studies of other galaxies, reinforcing the idea of using HII regions as standard candles.