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The Janus transition metal dichalcogenides intrinsically have Rashba spin splitting due to the presence of the out-of-plane mirror-symmetry breaking and strong spin-orbit coupling (SOC). Using first-principles calculations, we show that a van der Waals (vdW) heterostructure consisting of WSeTe and CrI₃ has inherently coexistence of Rashba and Zeeman spin splitting near the Brillouin zone center (Γ). The Rashba spin splitting states of WSeTe open an exchange gap of 29 meV when it is placed on the top of two-dimensional (2D) ferromagnetic semiconductor CrI₃. The spin-polarized subbands of Rashba-split states are separated at the Γ point because of the existence of effective perpendicular magnetic field stemmed from CrI₃. In the crossover region of Rashba and Zeeman spin splitting, the spin orientations of the two subbands are locked to the momenta. A single-circle Fermi contour could emerge if the Fermi level is tuned to locate exactly within the gap between the two subbands. Our results provide important insight into the manipulation of spin states for future spintronics applications of 2D vdW heterostructures.