Laser-induced periodic surface structures (LIPSS) are often present when processing solid targets with linearly polarized ultrashort laser pulses. The different irradiation parameters to produce them on metals, semiconductors and dielectrics have been studied extensively, identifying suitable regimes to tailor its properties for applications in the fields of optics, medicine, fluidics and tribology, to name a few. One important parameter widely present when exposing the samples to the high intensities provided by these laser pulses in air environment, that generally is not considered, is the formation of a superficial laser-induced oxide layer. In this paper, we fabricate LIPSS on a layer of the oxidation prone hard-coating material chromium nitride in order to investigate the impact of the laser-induced oxide layer on its formation. A variety of complementary surface analytic techniques were employed, revealing morphological, chemical and structural characteristics of well-known high-spatial frequency LIPSS (HSFL) together with a new type of low-spatial frequency LIPSS (LSFL) with an anomalous orientation parallel to the laser polarization. Based on this input, we performed finite-difference time-domain calculations considering a layered system resembling the geometry of the HSFL along with the presence of a laser-induced oxide layer. The simulations support a scenario that the new type of LSFL is formed at the interface between the laser-induced oxide layer and the non-altered material underneath. These findings suggest that LSFL structures parallel to the polarization can be easily induced in materials that are prone to oxidation.