For six years the Convection, Rotation, and planetary Transits (CoRoT) space mission has been acquiring photometric data from more than 100 000 point sources towards and directly opposite the inner and outer regions of the Galaxy. The high temporal resolution of the CoRoT data, combined with the wide time span of the observations, enabled the study of short- and long-time variations in unprecedented detail. The aim of this work is to study the variability and evolutionary behaviour of M-giant stars using CoRot data. From the initial sample of 2534 stars classified as M giants in the CoRoT databases, we selected 1428 targets that exhibit well defined variability, by visual inspection. Then, we defined three catalogues: C1 - stars with T_eff_<4200K and LCs displaying semi-sinusoidal signatures; C2 - rotating variable candidates with T_eff_>4200K; C3 - long-period variable candidates (with LCs showing a variability period up to the total time span of the observations). The variability period and amplitude of C1 stars were computed using Lomb-Scargle and harmonic fit methods. Finally, we used C1 and C3 stars to study the variability behaviour of M-giant stars. The trends found in the V-I vs. J-K colour-colour diagram are in agreement with standard empirical calibrations for M giants. The sources located towards the inner regions of the Galaxy are distributed throughout the diagram, while the majority of the stars towards the outer regions of the Galaxy are spread between the calibrations of M giants and the predicted position for carbon stars. The stars classified as supergiants follow a different sequence from the one found for giant stars. We also performed a Kolmogorov-Smirnov (KS) test of the period and amplitude of stars towards the inner and outer regions of the Galaxy. We obtained a low probability that the two samples came from the same parent distribution. The observed behaviour of the period-amplitude and period-effective temperature (T_eff_) diagrams are, in general, in agreement with those found for Kepler sources and ground based photometry, with pulsation being the dominant cause responsible for the observed modulation. We also conclude that short-time variations on M-giant stars do not exist or are very rare, and the few cases we found are possibly related to biases or background stars.