Incorporating advanced DFT methods is essential for accurately describing compression-driven magnetic and spin transitions in materials relevant to planetary interiors. Here, we present a first-principles investigation of the pressure-induced spin crossover in face-centered cubic (fcc) FeH using density functional theory with Hubbard U corrections (DFT + U). By evaluating how the choice of U affects the relative stability, volume, and magnetic moment of high-spin (HS) and low-spin (LS) solutions, we find that FeH remains in an HS ferromagnetic state up to ∼43 GPa with U = 3.00 eV, followed by a gradual crossover to an LS nonmagnetic state described by U = 1.07 eV and completed near ∼60 GPa. The static HS–LS endmember contrast produces distinct changes in volume, elastic stiffness, compressibility, density, and acoustic velocity, with the largest response observed in C11. The calculated bulk moduli of 164.3 GPa for the HS state and 227.4 GPa for the LS state, together with an approximately 13% density increase across the crossover, highlight the geophysical significance of FeH at core pressures. Enthalpy and cohesive-energy trends further support stabilization of the compressed LS state, and the static HS–LS endmember branches show a change in the pressure dependence of compressional velocity across the inferred crossover interval. These findings underscore the critical role of electron-correlation effects in controlling the spin-state energetics and static endmember elastic response of FeH, and establish FeH as a useful analogue for assessing the behavior of hydrogen-bearing iron phases in terrestrial planetary cores.