The formation of self-organized laser-induced periodic surface structures (LIPSS) in metals, semiconductors, and dielectrics upon pulsed laser irradiation is a well-known phenomenon, receiving increased attention because of their huge technological potential. For the case of metals, a major role in this process is played by surface plasmon polaritons (SPPs) propagating at the interface of the metal with the medium of incidence. Yet, simple and advanced models based on SPP propagation sometimes fail to explain experimental results, even of basic features such as the LIPSS period. We experimentally demonstrate, for the particular case of LIPSS on Cu, that significant deviations of the structure period from the predictions of the simple plasmonic model are observed, which are very pronounced for elevated angles of laser incidence. In order to explain this deviation, we introduce a model based on the propagation of SPPs on a rough surface that takes into account the influence of the specific roughness properties on the SPP wave vector. Good agreement of the modeling results with the experimental data is observed, which highlights the potential of this model for the general understanding of LIPSS in other metals.