The aim of the study was to manufacture poly(lactic acid)-(PLA-) based nanofibrous nonwovens that were modified using two types of modifiers, namely, gelatin-(GEL-) based nanofibres and carbon nanotubes (CNT). Hybrid nonwovens consisting of PLA and GEL nanofibres (PLA/GEL), as well as CNT-modified PLA nanofibres with GEL nanofibres (PLA + CNT/GEL), in the form of mats, were manufactured using concurrent-electrospinning technique (co-ES). The ability of such hybrid structures as potential scaffolds for tissue engineering was studied. Both types of hybrid samples and one-component PLA and CNTs-modified PLA mats were investigated using scanning electron microscopy (SEM), water contact angle measurements, and biological and mechanical tests. The morphology, microstructure, and selected properties of the materials were analyzed. Biocompatibility and bioactivity in contact with normal human osteoblasts (NHOst) were studied. The coelectrospun PLA and GEL nanofibres retained their structures in hybrid samples. Both types of hybrid nonwovens were not cytotoxic and showed better osteoinductivity in comparison to scaffolds made from pure PLA. These samples also showed significantly reduced hydrophobicity compared to one-component PLA nonwovens. The CNT-contained PLA nanofibres improved mechanical properties of hybrid samples and such a 3D system appears to be interesting for potential application as a tissue engineering scaffold.