In this study, the structure, electrical and thermal properties of ten polymer compositions based on polylactic acid (PLA), low-cost industrial graphene nanoplates (GNP) and multi-walled carbon nanotubes (MWCNT) in mono-filler PLA/MWCNT and PLA/GNP systems with 0–6 wt.% filler content were investigated. Filler dispersion was further improved by combining these two carbon nanofillers with different geometric shapes and aspect ratios in hybrid bi-filler nanocomposites. Scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Raman spectroscopy exhibited uniform dispersion of nanoparticles in a polymer matrix. The obtained results have shown that for the mono-filler systems with MWCNT or GNP, the electrical conductivity increased with decades. Moreover, a small synergistic effect was observed in the GNP/MWCNT/PLA bi-filler hybrid composites when combining GNP and CNT at a ratio of 3% GNP/3% CNT and 1.5% GNP:4.5% CNT, showing higher electrical conductivity with respect to the systems incorporating individual CNTs and GNPs at the same overall filler concentration. This improvement was attributed to the interaction between CNTs and GNPs limiting GNP aggregation and bridging adjacent graphene platelets thus, forming a more efficient network. Thermal conductivity increases with higher filler content; this effect was more pronounced for the mono-filler composites based on PLA and GNP due to the ability of graphene to better transfer the heat. Morphological analysis carried out by electron microscopy (SEM, TEM) and Raman indicated that the nanocomposites present smaller and more homogeneous filler aggregates. The well-dispersed nanofillers also lead to a microstructure which is able to better enhance the electron and heat transfer and maximize the electrical and thermal properties. The obtained composites are suitable for the production of a multifunctional filament with improved electrical and thermal properties for different fused deposition modelling (FDM) 3D printing applications and also present a low production cost, which could potentially increase the competitiveness of this promising market niche.