This research aims to develop fiber-reinforced composites (FRC) with enhanced fire resistance, which can be particularly useful for the transport industry (e.g., aviation, automotive, and train production). The fire retardation was achieved through epoxy matrix modification with hexachlorocyclotriphosphazene (HCTP). First, the fire-resistant and mechanical properties of the epoxy matrix filled with different HCTP contents (4.8, 7.2, and 9.5 wt.%) were studied to select the most effective HCTP content for the impregnation of FRC. Then, glass, basalt, and carbon fiber fabrics were impregnated with epoxy filled with 7.2 wt.% of HCTP, and the fire resistance, flexural, and interlaminar fracture properties were studied to select the most effective HCTP-modified type of fiber reinforcement based on the test results. It was concluded that basalt fiber impregnated with epoxy filled with HCTP could be selected as the most effective reinforcement type, allowing excellent mechanical and flame-retardant properties.