Ultrafast processes can now be studied with the combined atomic spatial resolution of diffraction methods and the temporal resolution of femtosecond optical spectroscopy by using femtosecond pulses of electrons or hard X-rays as structural probes. However, it is challenging to apply these methods to organic materials, which have weak scattering centres, thermal lability, and poor heat conduction. These characteristics mean that the source needs to be extremely bright to enable us to obtain high-quality diffraction data before cumulative heating effects from the laser excitation either degrade the sample or mask the structural dynamics. Here we show that a recently developed, ultrabright femtosecond electron source makes it possible to monitor the molecular motions in the organic salt (EDO-TTF)2PF6 as it undergoes its photo-induced insulator-to-metal phase transition. After the ultrafast laser excitation, we record time-delayed diffraction patterns that allow us to identify hundreds of Bragg reflections with which to map the structural evolution of the system. The data and supporting model calculations indicate the formation of a transient intermediate structure in the early stage of charge delocalization (less than five picoseconds), and reveal that the molecular motions driving its formation are distinct from those that, assisted by thermal relaxation, convert the system into a metallic state on the hundred-picosecond timescale. These findings establish the potential of ultrabright femtosecond electron sources for probing the primary processes governing structural dynamics with atomic resolution in labile systems relevant to chemistry and biology.