Implementing superconductors capable of proximity-inducing a large energy gap in semiconductors in the presence of strong magnetic fields is a major goal toward applications of semiconductor/superconductor hybrid materials in future quantum information technologies. Here, we study the performance of devices consisting of InAs nanowires in electrical contact with molybdenum-rhenium (MoRe) superconducting alloys. The MoRe thin films exhibit transition temperatures of similar to 10 K and critical fields exceeding 6 T. Normal/superconductor devices enabled tunnel spectroscopy of the corresponding induced superconductivity, which was maintained up to similar to 10 K, and MoRebased Josephson devices exhibited supercurrents and multiple Andreev reflections. We determine an induced superconducting gap lower than expected from the transition temperature and observe gap softening at finite magnetic field. These may be common features for hybrids based on large-gap, type II superconductors. The results encourage further development of MoRe-based hybrids.