Aims. We use kinematical and chemical properties of 754 CoRoT stars to characterise the stellar populations of the Milky Way disc in three beams close the Galactic plane. Methods. From the atmospheric parameters derived in Gazzano et al. (2010, A&A, 523, A91) with the MATISSE algorithm, we derived stellar distances using isochrones. Combining these data with proper motions, we provide the complete kinematical description of stars in three CoRoT fields. Finally, we used kinematical criteria to identify the Galactic populations in our sample and study their characteristics, particularly their chemistry. Results. Comparing our kinematics with the Besancon Galactic model, we show that, within 3 sigma, simulated and observed kinematical distributions are in good agreement. We study the characteristics of the thin disc, finding a correlation that is significant at a value of 2-sigma between the V-velocity component and the metallicity for two different radial distance bins (8-9 kpc and 9-10 kpc; but not for the most inner bin 7-8 kpc, probably because of the uncertainties in the abundances), which could be interpreted as radial migration evidence. We also measured a radial metallicity gradient value of -0.097 +/- 0.015 dex kpc(-1) with giant stars, and -0.053 +/- 0.015 dex kpc(-1) with dwarfs. Finally, we identified metal-rich stars with peculiar, high [alpha/Fe] values in the directions pointing to the inner part of the Galaxy Applying the same methodology to the planet-hosting stars detected by CoRoT shows that they mainly belong to the thin disc population with normal chemical and kinematical properties.