Finite-Relaxation Geometry (FRG) 3.0 is formulated as a macroscopic effective cosmological framework in which large-scale spacetime geometry approaches quasi-stationary General Relativity configurations over a finite relaxation timescale. The Einstein–Hilbert action remains unmodified, and no additional propagating degrees of freedom are introduced. The relaxation parameter operates exclusively at homogeneous cosmological scales and vanishes in the high-curvature regime, ensuring exact recovery of standard General Relativity in the early universe. The framework preserves local Lorentz invariance, causal structure, weak-field gravity, and gravitational wave propagation properties. Background stability, conservation consistency, linear perturbation behavior, and tensor-mode dynamics are explicitly analyzed. FRG introduces a controlled phenomenological relaxation parameter without modifying the kinetic structure of gravity. Finite-Relaxation Geometry is presented as a conservative effective extension of cosmological modeling. Its validity is subject to observational testing through high-precision measurements of late-time expansion dynamics.