Considering that the ferritic stainless steel Z10C13 support plate material in nuclear power equipment tends to undergo fretting wear during service, this paper systematically investigates the effect of varying normal loads (10–50 N) and displacement amplitudes (15–75 μm) on its fretting response and wear mechanisms. Through ball-on-flat fretting wear experiments, together with macro- and micro-scale observations of wear scars, it is revealed that normal load primarily controls the contact intensity and the extent of adhesion, whereas displacement amplitude mainly affects the slip amplitude and features of fatigue damage. The results show that the fretting system’s dissipated energy increases nonlinearly with both load and amplitude, and their coupled effect significantly exacerbates interfacial damage. The wear scar morphology evolves from a shallow bowl shape to a structure characterized by multiple spalling pits and propagating fatigue cracks. An equivalent hardness-corrected Archard model is proposed based on the experimental data. The model captures the nonlinear dependence of equivalent material hardness on both load and amplitude. As a result, it accurately predicts wear volume ($R^2=0.9838$), demonstrating its physical consistency and modeling reliability. Overall, this study elucidates the multi-scale damage evolution mechanism of Z10C13 under fretting conditions and provides a theoretical foundation and methodological support for wear-resistant design, life prediction, and safety evaluation of nuclear power support structures.