For 6 years the Convection, Rotation, and Planetary Transits (CoRoT) space mission has acquired photometric data from more than one hundred thousand point sources towards and directly opposite from 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 has enabled the study of short and long time variations in unprecedented detail. From the initial sample of 2534 stars classified as M-giants in the CoRoT databasis, we selected 1428 targets that exhibit well defined variability, using visual inspection. The variability period and amplitude of C1 stars (stars having Teff < 4200 K) were computed using Lomb-Scargle and harmonic fit methods. The trends found in the V-I vs J-K color-color 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 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 come from the same parent distribution. The observed behavior of the period-amplitude and period-Teff 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 orare very rare and the few cases we found are possibly related to biases or background stars.