The organic salt β″-(BEDT-TTF)₂SF₅CH₂CF₂SO₃ is a two-dimensional metal with a quarter-filled conduction band. In the metallic state the optical conductivity evidences interaction of the charge carriers with charge-order fluctuations that become stronger as temperature decreases. In the superconducting phase below T_c≈5K, indications of the superconducting gap with 2Δ≈12cm^-1 are observed in the optical spectrum, corresponding to 2Δ≈/k_B T_c≈3.3. Its temperature and magnetic field dependences are also consistent with predictions by the BCS theory of a weakly coupled superconductor. The conductivity ratio σ₁1(T = 1:75 K)/σ₁(10 K) indicates the opening of the superconducting gap in β″-(BEDT-TTF)₂SF₅CH₂CF₂SO₃.