We measure the spectrum of coherent Brillouin scattering (CBS) in a gas as a function of time and observe for the first time additional spectral sidebands and line shape narrowing of the Brillouin peak. We find that both effects result from the interference of the density modulation induced by the moving dipole force of the pump beams with the acoustic waves induced by their fast thermalization and are predicted by a hydrodynamic-light scattering model. These line shapes differ from both spontaneous and stimulated Brillouin scattering spectra and also from previous coherent Rayleigh-Brillouin measurements.