This article’s aim is to analyze physical, mechanical, and fracture properties as well as the thermal investigation of geopolymer composites reinforced with flax, glass fiber, and also the hybrid combination of fibers. Two types of matrices were considered as composites matrices. The first composition was based on fly ash and river sand. The second matrix composition contained fly ash and glass spheres. The content of reinforcement was 1% by mass. Compressive strength and three-point bending fracture tests were performed. The values of fracture toughness and fracture energy were determined. The resonance method was used to verify the dynamic characteristics, such as the dynamic modulus of elasticity and the dynamic Poisson ratio. The results show that single-type fibers in composites based on fly ash and glass spheres did not affect compressive strength. However, introducing hybrid reinforcement increased compressive strength by about 10% compared to the reference specimens. Flax fibers and hybrid reinforcement ensured higher fracture toughness and energy. The results also revealed great potential for glass sphere application to geopolymer materials in terms of fracture mechanics and thermal properties. Despite the lower strength properties in relation to geopolymers based on sand aggregate, applying reinforced fibers into the composite with glass spheres enhanced the compressive strength compared to other materials. Materials modified with glass spheres have a thermal conductivity twice as low as that of materials containing river sand.