To promote the sustainable development of the ecological environment, facilitate the recycling of recycled concrete and explore efficient approaches to enhance the performance of structural components, this study proposes a post-tensioned precast beam model manufactured with basalt-fiber-reinforced recycled concrete–conventional concrete. Flexural performance tests were conducted on 12 beams with different concrete strength grades (C40, C50, C60), basalt-fiber-reinforced recycled concrete layer thicknesses (200 mm, 250 mm, 300 mm), and basalt fiber volume fractions (0%, 0.1%, 0.2%). The results show that the incorporation of basalt fiber can effectively inhibit crack development, and improve the stiffness and flexural strength of components. Through theoretical analysis, the factors affecting the ultimate stress formula for high-strength prestressing steel strands are attributed to the comprehensive reinforcement index and prestressed reinforcement index, thereby obtaining a flexural strength formula. Coefficients describing the influences of basalt fiber and recycled coarse aggregate were introduced and combined with average crack spacing and width measurements to derive a post-tensioned precast beam model of average crack spacing and width. Based on the derived calculation model, the average deviation between the tested and calculated results of the ultimate bending moment is less than 6%, and the average deviation between the tested and calculated results of the average crack width is less than 9%. The proposed model has good prediction accuracy for evaluating the flexural strength and average crack width, which provides a theoretical basis for assessing the flexural performance of composite beams.