The new capacity of X-ray free-electron laser (XFEL) facilities to produce multi-color X-ray femtosecond pulses paves the way to explore ultrafast phenomena in matter induced by X-ray photons. In the present study, we exploit the site-selectivity and the high temporal resolution of a two-color X-ray femtosecond pump-probe sequence to investigate the isomerization of formamide. The pump pulse excites a particular atomic site in the molecule, while the probe pulse captures changes in the chemical environment at a remote atomic site. The response of the system is found to strongly depend on the nature of the excited site, and the core excitation provides selective control over chemical bond breaking. In particular, we show that the N1s → π* transition can induce the isomerization reaction in formamide and demonstrate the possibility to observe in real time hydrogen migration by measuring the chemical shifts with the X-ray probe pulse. This work opens a unique prospect for X-ray-induced photochemistry at XFEL facilities.