Fuel cell systems require high-efficiency DC–DC interfaces capable of regulating rapid voltage variations while respecting the operational constraints of proton-exchange membrane fuel cells (PEMFCs). The floating interleaved boost converter (FIBC) is a strong candidate for this purpose due to its reduced current ripple, improved power sharing, and lower component stress. The design of control strategies for FIBCs supplied by PEMFCs remains challenging because explicitly enforcing fuel cell operational constraints under fast converter dynamics is inherently difficult, particularly when detailed fuel cell models are unavailable or undesirable, as reflected in existing approaches such as classical linear regulators and single-model predictive schemes. Therefore, this paper proposes a multi-model finite control set model-based predictive control (MM-FCS-MPC) strategy for FIBC converters supplied by PEMFCs. The method employs multiple discrete prediction models with cost functions defined by the converter switching mode, integrates a fuel cell-aware reference-generation mechanism to ensure nominal and safe PEMFC operation by enforcing current and power constraints within the predictive framework, and enables fast, accurate output-voltage regulation. Detailed modelling of the FIBC, component sizing, and PEMFC characteristics is provided. Obtained results under load disturbances and reference variations validate the proposed control scheme, demonstrating improved transient dynamics, reduced steady-state error, and enhanced current-sharing performance. Obtained results under load disturbances and reference variations validate the proposed control scheme, demonstrating improved transient dynamics, reduced steady-state error, and enhanced current-sharing performance, with a rise time of approximately 4.4 ms, a $\pm 2\%$ settling time of 10.3 ms, a maximum overshoot of only 0.056%, and a phase delay of approximately 4.26°, compared with 9.6° for the conventional PI voltage-tracking baseline.