In connection with experiments aiming at the improvement of the cesium atomic beam clock by means of a fountain of laser-cooled cesium atoms, we present expressions for the line shift and line broadening due to collisions between cesium atoms. The coherent collision cross sections occurring in these expressions are calculated by means of the coupled-channels method. The magnitude of the calculated shift implies that spin-exchange collisions are an important factor in limiting the anticipated accuracy of a future cesium fountain clock and of other intended fountain experiments.