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Abstract A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. In this work, we present such a case: we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in JJs and observe a deviation from the standard CPR. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. The analysis examines how multiband effects and the experimentally visualized ferroelectric domain walls give rise to this behavior, giving insight into the Josephson effect in materials that possess ferroelectricity and/or multiband superconductivity.