Track–bridge interaction (TBI) is an increasingly essential consideration for the design and operation of railway bridges, especially for the innovative bridge structure systems that constantly spring up over the years. This paper focuses on the characteristics of additional forces in continuous welded rails (CWRs) on the 3 × 70 m integral rigid-frame bridge of the Fuzhou–Xiamen High-Speed Railway, which is a novel high-speed railway (HSR) bridge structure system in China. The differential equations of rail stress and displacement are first investigated and an integrative analysis model comprising of rail, track, bridge and piers is then established. Secondly, the characteristics of representative additional forces are illustrated and the influences of different design parameters are discussed in detail. Furthermore, suitable rail fasteners, optimal layout schemes of adjacent bridges and reasonable stiffness of piers are also studied. The results indicate that the additional expansion force accounts for the largest proportion of additional forces in integral rigid-frame bridges and that resistance reduction obviously weakens the various additional forces caused by the TBI effect, while the broken gap of the rail increases greatly. Small resistance fasteners are recommended to be applied onto this new type of HSR line as these provide reductions in additional stresses of CWRs compared to WJ-8 fasteners. The additional rail stresses after adopting an adjacent span scheme of 4 × 32 m simply supported beams are less than the corresponding stresses in other schemes. The results also show that there is a strong correlation between the minimum threshold value of the pier stiffness and the longitudinal resistance of HSR lines for the integral rigid-frame bridge. This work could serve as a valuable reference for detailed design and safety evaluation of integral rigid-frame bridges.