Recalcitrant compounds resulting from anthropogenic activity are a significant environmental challenge, necessitating the development of advanced oxidation processes (AOPs) for effective remediation. This study explores the synthesis of cuprous oxide nanoparticles on cellulose-based paper (Cu2O@CBP) using Eucalyptus globulus leaf extracts, leveraging green synthesis techniques. The scanning electron microscopy (SEM) analysis found the average particle size 64.90 ± 16.76 nm, X-ray diffraction (XRD) and Raman spectroscopy confirm the Cu2O structure in nanoparticles; Fourier-transform infrared spectroscopy (FTIR) suggests the reducing role of phenolic compounds; and ultraviolet–visible diffuse reflectance spectroscopy (UV-Vis DRS) allowed us to determine the band gap (2.73 eV), the energies of the valence band (2.19 eV), and the conduction band (−0.54 eV) of Cu2O@CBP. The synthesized Cu2O catalysts demonstrated efficient degradation of methylene blue (MB) used as a model as recalcitrant compounds under LED-driven visible light photocatalysis and heterogeneous Fenton-like reactions with hydrogen peroxide (H2O2) using the degradation percentage and the first-order apparent degradation rate constant (kapp). The degradation efficiency of MB was pH-dependent, with neutral pH favoring photocatalysis (kapp = 0.00718 min−1) due to enhanced hydroxyl (·OH) and superoxide radical (O2·−) production, while acidic pH conditions improved Fenton-like reaction efficiency (kapp = 0.00812 min−1) via ·OH. The reusability of the photocatalysts was also evaluated, showing a decline in performance for Fenton-like reactions at acidic pH about 22.76% after five cycles, while for photocatalysis at neutral pH decline about 11.44% after five cycles. This research provides valuable insights into the catalytic mechanisms and supports the potential of eco-friendly Cu2O nanoparticles for sustainable wastewater treatment applications.