We present the G0W0 band structure, core levels, and deformation potential of monolayer FeSe in the paramagnetic phase based on a starting mean field of the Kohn-Sham density functional theory (DFT) with the Perdew, Burke, and Ernzerhof functional. We find the GW correction increases the bandwidth of the states forming the M pocket near the Fermi energy, while leaving the Γ pocket roughly unchanged. We then compare the G0W0 quasiparticle band energies with the band structure from a simple empirical +A approach, which was recently proposed to capture the renormalization of the electron-phonon interaction going beyond DFT in FeSe, when used as a starting point in density functional perturbation theory. We show that this empirical correction succeeds in approximating the GW nonlocal and dynamical self-energy in monolayer FeSe and reproduces the GW band structure near the Fermi surface, the core energy levels, and the deformation potential (electron-phonon coupling).