One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction is π-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman-effect-induced 0-π transitions in Bi_{1-x}Sb_{x}, three-dimensional Dirac semimetal-based Josephson junctions. The large in-plane g factor allows tuning of the Josephson junctions from 0 to π regimes. This is revealed by measuring a π phase shift in the current-phase relation measured with an asymmetric superconducting quantum interference device (SQUID). Additionally, we directly measure a nonsinusoidal current-phase relation in the asymmetric SQUID, consistent with models for ballistic Josephson transport.