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C3 is a molecular chain which has been observed in interstellar clouds and in comets. It is also a very floppy molecule for which the vibrational bending transitions are in the same energy range as the rotational transitions. In this paper, we apply our recently developed quantum scattering method for treating atom rigid bender inelastic collisions at the Close Coupling level to the collision of C3 by helium. This method allows us to compute the rovibrational transitions induced by collisions. The purely rotational transitions have been also calculated, using the rigid monomer approximation. The accuracy of this last approximation in the case of a system with a significant vibrational-rotational coupling is discussed. The first evaluation of the cross-sections associated with the rovibrational transitions between levels belonging to different vibrational bending levels is also presented. We observe that the propensity rule for the rovibrational transitions is a competition between the smallest Δj and the smallest transition energy. As a consequence, cross-sections and rate coefficients of vibrationally inelastic transitions can be several orders of magnitude larger than for purely rotational transitions.