The study and utilization of fully recycled aggregate concrete (FRAC), in which coarse and fine aggregates are completely replaced by recycled aggregates, are of great significance in improving the recycling rate of construction waste, reducing the carbon emission of construction materials, and alleviating the ecological degradation problems currently faced. In this paper, investigations were carried out to study the effects of steel fiber (0.5%, 1.0%, and 1.5%) and polypropylene fiber (0.9 kg/m³, 1.2 kg/m³ and 1.5 kg/m³) on the properties of FRAC, including compressive strength, splitting tensile strength, the splitting tensile load–displacement curve, the tensile toughness index, flexural strength, the load–deflection curve, and the flexural toughness index. The results show that the compressive strength, splitting tensile strength, and flexural strength of fiber-reinforced FRAC were remarkably enhanced compared with those of ordinary FRAC, and the maximum increase was 56.9%, 113.3%, and 217.0%, respectively. Overall, the enhancement effect of hybrid steel–polypropylene fiber is more significant than single-mixed fiber. Moreover, the enhancement of the crack resistance, tensile toughness, and flexural toughness obtained by adding steel fiber to the FRAC is more significant than that obtained by adding polypropylene fiber. Furthermore, adding polypropylene fiber alone and mixing it with steel fiber showed different FRAC splitting tensile and flexural properties.