Indonesia generates large quantities of agro-industrial waste, including oil palm empty fruit bunch (OPEFB) and sugarcane bagasse, which have potential as sustainable reinforcing materials for polymer composites. This study investigated the effect of OPEFB–bagasse fibre composition on the mechanical properties of epoxy-based hybrid composites fabricated using the hand lay-up method. Five composite formulations with a constant epoxy content of 50% and varying OPEFB-to-bagasse ratios were prepared and evaluated through tensile, flexural, impact, and scanning electron microscopy (SEM) analyses. The hybrid composite containing 30% OPEFB, 20% bagasse, and 50% epoxy exhibited the best overall mechanical performance, achieving a tensile strength of 16.78 MPa, a flexural strength of 59.95 MPa, an impact toughness of 3.08 kJ/m², and a Young's modulus of 8.80 GPa. SEM observations revealed good fibre–matrix adhesion and fibre pull-out mechanisms that contributed to improved energy absorption. Statistical analysis showed that fibre composition significantly affected flexural strength (p = 0.047), whereas its effects on tensile strength and impact toughness were not statistically significant (p > 0.05). The developed hybrid composite exhibited mechanical properties comparable to several previously reported natural fibre-reinforced epoxy composites, indicating its potential for lightweight non-structural automotive body applications.