Ultrafast dynamics of the light-matter interaction in a charge-ordered molecular insulator α-(BEDT-TTF)2I3 were studied by pump-probe spectroscopy using few-optical-cycle infrared pulses (pulse width 12 fs). Coherent oscillation of the correlated electrons and subsequent Fano destructive interference with intramolecular vibration were observed in time domain; the results indicated a crucial role for electron-electron interplay in the light-matter interaction leading to the photoinduced insulator-to-metal transition. The qualitative features of this correlated electron motion were reproduced by calculations based on exact many-electron-phonon wave functions.