We present high-resolution near-edge X-ray absorption fine structure (NEXAFS) measurements at the P L2/3 edges, F K edge, C K edge, and Se M2/3 edges of the quasi-one-dimensional (1D) conductor and superconductor (TMTSF)2PF6. NEXAFS allows probing the donor and acceptor moieties separately; spectra were recorded between room temperature (RT) and 30 K at normal incidence. Spectra taken around RT were also studied as a function of the angle (θ) between the electric field of the X-ray beam and the 1D conducting direction. In contrast with a previous study of the S L2/3-edges spectra in (TMTTF)2AsF6, the Se M2/3 edges of (TMTSF)2PF6 do not exhibit a well-resolved spectrum. Surprisingly, the C K-edge spectra contain three well-defined peaks exhibiting strong and nontrivial θ and temperature dependence. The nature of these peaks as well as those of the F K-edge spectra could be rationalized on the basis of first-principles DFT calculations. Despite the structural similarity, the NEXAFS spectra of (TMTSF)2PF6 and (TMTTF)2AsF6 exhibit important differences. In contrast with the case of (TMTTF)2AsF6, the F K-edge spectra of (TMTSF)2PF6 do not change with temperature despite stronger donor-anion interactions. All these features reveal subtle differences in the electronic structure of the TMTSF and TMTTF families of salts.