Modulating electron-phonon coupling offers a route to control structural displacements and tune material functionality. Valence-to-conduction band transitions, however, provide limited leverage over the driving force. Here, we demonstrate coherent lattice dynamics in trigonal tellurium using free-electron laser pulses tuned to the Te N4,5-edge. Over a broad fluence range, the oscillation amplitude obeys the displacive excitation of coherent phonons framework, extended to core resonance with twice the driving efficiency of a visible pump. Ab initio calculations decompose the force into competing multiband contributions, inaccessible to optical excitation, whose balance shifts as carriers relax. Tunable extreme-ultraviolet and X-ray pulses thus open a regime in which the displacive response is set by band-dependent coupling to the lattice, not by the number and temperature of the photocarriers alone.