A theoretical investigation of the Zeeman (Ze) splittings and the magnetization of Fr2+ ions in semimagnetic semiconductors (SMSC) having the zinc-blende (e.g., CdTe) and the wurtzite (e.g., CdSe) structure is presented. The Hamiltonian matrix is constructed within the D-5 term of a 3d(4) or 3d(6) ion by considering the trigonal crystal-field (CF). the spin-orbit (SO), the spin-spin (SS) and the Ze interactions. The values of the CF, SO and SS parameters are obtained by fitting the theoretical predictions to the available optical and fine-structure experimental data. The contribution of the SS coupling to the fine-structure splittings of the ground state in these systems is found to be important. The Ze energy levels and the magnetization are studied as functions of the magnetic field B in the range 0-40 T applied in the direction [111], [110] and [100] for CdTe:Fe2+ and in the direction parallel and perpendicular to the crystal c-axis for CdSe:Fe2+. The theoretical results reveal some energy level crossings and the related magnetic anisotropy in SMSC, especially at high magnetic fields. The B --> infinity limit, where the Zeeman term dominates, has also been analyzed.