The electron-doped ${\text{Pr}}_{2\ensuremath{-}x}{\text{Ce}}_{x}{\text{CuO}}_{4}$ (PCCO) compound in the pseudogap regime $(x\ensuremath{\approx}0.15)$ was investigated using the angle-resolved photoemission spectroscopy and the generalized dynamical mean-field theory (DMFT) with the $\mathbf{k}$-dependent self-energy $(\text{LDA}+\text{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}})$. Model parameters (hopping integral values and local Coulomb interaction strength) for the effective one-band Hubbard model were calculated by the local-density approximation (LDA) with numerical renormalization-group method employed as an ``impurity solver'' in DMFT computations. An ``external'' $\mathbf{k}$-dependent self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$ was used to describe interaction of correlated conducting electrons with short-range antiferromagnetic (AFM) pseudogap fluctuations. Both experimental and theoretical spectral functions and Fermi surfaces were obtained and compared demonstrating a good semiquantitative agreement. For both experiment and theory normal-state spectra of nearly optimally doped PCCO show clear evidence for a pseudogap state with AFM-like nature. Namely, folding of quasiparticle bands as well as the presence of the ``hot spots'' and ``Fermi arcs'' was observed.