The band structures of pure and hole doped La2CuO4 with antiferromagnetic (AFM) spin fluctuations are calculated and compared to spectral weights of angle-resolved photoemission spectroscopy (ARPES). It is shown that observations of coexisting Fermi-surface (FS) arcs and closed FS pockets are consistent with modulated AFM spin fluctuations of varying wavelengths. Large variations of strong spin fluctuations make the outer part of the FS break diffuse at low doping. This part of the FS is suppressed at high doping when spin fluctuations are weak. The resulting superimposed spectral weight has features both from FS arcs and closed pockets. A connection between results of ARPES, neutron scattering, and band results for the modulated AFM spin-wave state suggests that spin-phonon coupling is an important mechanism for the properties of the cuprates.