The residual biomass of cold-pressed green coffee oil (GCO), rich in chlorogenic acids (CGA), was reused by incorporating the press cake (CE) and sediment (SE) extracts into carboxymethyl cellulose (CMC) films. The effect of these extracts combined with GCO was investigated on the physicochemical, barrier, and antioxidant properties, and on the ability of the active films to delay fish oil oxidation. The films with added CE and GCO (C-CE) or SE and GCO (C-SE) showed high antioxidant activity, 3.61 ± 0.01 and 2.03 ± 0.01 mmol Trolox eq/g dry film, respectively. These findings are in line with the CGA content in CE and SE (9.8 and 9.0% w/w, respectively), as determined by HPLC. The addition of SE and GCO slightly affects the oxygen barrier of CMC films, while providing them with high Ultraviolet–Visible (UV–Vis) absorption. The evolution of peroxide value (PV) and thiobarbituric acid reactive substances (TBARS) in fish oil samples covered by C-CE and C-SE films and inert headspace was significantly lower than those of controls (storage at 40 °C for 16 days). The antioxidant release from films with added CE and SE showed an antagonistic behaviour into the food simulants. Although both active films are promising for active packaging, the C-SE film appeared as more advantageous for oil-rich food protection.