The microlensing event Gaia20fnr is a long-duration, non-caustic-crossing binary-lens event located at high Galactic latitude. Triggered by a photometric rise detected by the Gaia space mission, the event was followed up with observations from multiple ground-based facilities and observed by four space telescopes: Gaia, NEOWISE, Swift, and TESS. We characterize the Gaia20fnr microlensing system by determining the physical and orbital properties of the binary lens, the nature of the luminous source, and the kinematics of both the source and the lens. We employed a binary-lens microlensing model including full Keplerian orbital motion and annual microlens parallax to fit the photometric data. The event is best explained by a K2 giant source at D_S_=3.10+/-0.10kpc lensed by a stellar binary composed of M_L,1_=0.46+/-0.06M_{sun} and M_L,2=0.52+/-0.06M_{sun} at a distance of D_L=0.54+/-0.05kpc. The light curve exhibits strong signatures of orbital motion and requires a full Keplerian model with a period of P=0.67+/-0.04yr and a radial-velocity semi-amplitude of K_1_=16.9+/-0.9km/s to be explained. Gaia20fnr is one of the few microlensing events for which a complete Keplerian binary-lens solution has been derived. The model can be tested with follow-up radial-velocity and high-resolution imaging observations as well as forthcoming Gaia DR4 and DR5 astrometric time-series data. Its long duration, multi-peak structure, and extensive coverage from both space- and ground-based facilities make it a benchmark for studying faint nearby low-mass binaries through microlensing.