Greener materials, particularly in sandwich panels, are in increasing demand in the transportation and building sectors to reduce environmental impacts. This shift is driven by strict environmental legislation and the need to reduce material costs and fuel consumption, necessitating the utilisation of more sustainable components in the transportation and construction sectors, with improved load-bearing capabilities and diminished ecological footprints. Therefore, this study aims to analyse and evaluate the structural performance of polyethylene terephthalate (PET) core and flax or basalt/flax FRP sandwich panels as an alternative to conventional synthetic materials. The novel eco-friendly sandwich panels were manufactured using the co-curing technique. Four-point bending, edgewise compression and core shear tests were performed and insights into how the skin properties affect the strength, stiffness and failure mode of specimens were provided. The stress–strain behaviour, facing modulus and strength, flexural rigidity, core shear strength and failure modes were evaluated. The flexural facing modulus of the flax and flax/basalt sandwich skins were found to be 5.1 GPa and 9.8 GPa, respectively. The flexural rigidity of the eco-friendly sandwich panel was compared with published results and demonstrated a promising structural performance. The environmental benefits and challenges were outlined and critically evaluated focusing on transportation and construction applications.