A model of the reflected fringe system for an ideal plane-parallel, low-finesse Fabry-Perot (FP) cavity illuminated by a multimode optical fiber has been developed and experimentally validated. This showed that the phase dispersion within the cavity arising from the divergent nature of the incident illumination significantly degrades the visibility of the reflected fringes. Departures from the ideal FP cavity are also examined. The effect on fringe visibility when the plane of the FP cavity is tilted with respect to the fiber axis and when the cavity surfaces are no longer perfectly parallel to each other has been explored. The analysis described is relevant to the design and the optimization of multimode optical-fiber sensors that use FP sensing cavities.