Ultrashort light pulses can selectively excite charges, spins and phonons in materials, providing a powerful approach for manipulating their properties. Here we use femtosecond laser pulses to coherently manipulate the electron and phonon distributions, and their couplings, in the charge density wave (CDW) material 1T-TaSe$_2$. After exciting the material with a short light pulse, spatial smearing of the electrons launches a coherent lattice breathing mode, which in turn modulates the electron temperature. This indicates a bi-directional energy exchange between the electrons and the strongly-coupled phonons. By tuning the laser excitation fluence, we can control the magnitude of the electron temperature modulation, from ~ 200 K in the case of weak excitation, to ~ 1000 K for strong laser excitation. This is accompanied by a switching of the dominant mechanism from anharmonic phonon-phonon coupling to coherent electron-phonon coupling, as manifested by a phase change of $pi$ in the electron temperature modulation. Our approach thus opens up possibilities for coherently manipulating the interactions and properties of quasi-2D and other quantum materials using light.