The nucleoprotein filament (NPF) is the fundamental element of homologous recombination (HR), a major mechanism for the repair of double-strand DNA breaks in the cell. The NPF is made of the damaged DNA strand surrounded by recombinase proteins, and its sensitivity to base-pairing mismatches is a crucial feature that guarantees the fidelity of the repair. The concurrent recombinases are also essential for several steps of HR. In this work, we used torque-sensitive magnetic tweezers to probe and apply mechanical constraints to single nucleoprotein filaments (NPFs). We demonstrated that the NPF undergoes structural transitions from a stretched to a compact state, and we measured the corresponding mechanochemical signatures. Using an active two-state model, we proposed a free-energy landscape for the NPF transition. Using this quantitative model, we explained both how the sensitivity of the NPF to the homology length is regulated by its structural transition and how the cooperativity of Rad51 favors selectivity to relatively long homologous sequences.