Graphitic carbon nitride (g-C3N4) was used to enhance the photocatalytic activity of ZnO nanoparticles for the degradation of 5-fluorouracil (5-FU) cytostatic drug under UV-LED irradiation. CN/ZnO composites were synthetized by an easy one-pot thermal method, varying the g-C3N4 loading, i.e., from 10 to 67 wt% and a post-thermal exfoliation in air. The physicochemical and optical properties of the materials were analyzed by several techniques. CN/ZnO composites showed a coral-like structure of spherical ZnO wurtzite particles on the g-C3N4 structure. In general, the synergism and heterojunction interface between both phases allowed the enhancement of the mesoporosity, light absorption ability, and the aromaticity of the corresponding composites. Moreover, the photocatalytic activity of the CN/ZnO composites was increased with the addition of g-C3N4 in comparison with pristine ZnO. The highest activity was found for the composite containing 25 wt% of g-C3N4 (i.e., CN25/ZnO), reaching the total degradation of 5-FU and a mineralization of 48% at 180 min, as well as a good photostability during four reuse cycles. Experiments with different pH solutions and scavengers allowed for the assessment of the reactive oxygen species (ROS) involved in the 5-FU degradation pathway, with radicals and non-radical species as the main responsible active species. Furthermore, a tentative photocatalytic mechanism was proposed for CN/ZnO composites.