Ceramic matrix composite (CMC) components enable high turbine entry temperatures, which can lead to improved efficiencies in gas turbines. Implementing film cooling over CMC components, similar to how it is employed for conventional metal components, can extend part life and push operating temperatures beyond the temperature capabilities of CMCs alone. However, CMCs have a unique surface topology that can influence film cooling performance. Often this topology takes the form of an irregular wavy pattern due to the weave of the fibers that make up the strengthening component of the composite. In this study, shaped 7–7–7 film cooling holes are embedded in a five-harness-satin weave pattern representative of a CMC, at two orientations of the pattern. Detailed adiabatic film effectiveness measurements are obtained in a wind tunnel using an infrared camera while near-wall flowfield measurements are obtained with a high-speed particle image velocimetry system. A range of blowing ratios between one and three are investigated at a density ratio of 1.5 and freestream turbulence intensities of 0.5% and 13%. Across the majority of the tested conditions, the CMC surfaces result in lower film cooling performance than a smooth surface. At a freestream turbulence intensity of 0.5%, the adiabatic film effectiveness is moderately insensitive to the blowing ratio for both weave orientations. The boundary layer over the CMC surfaces increases the mixing between the coolant and the mainstream through a combination of increased turbulence, reduced near-wall velocities, and a thicker boundary layer.