Magnons are quanta of spin waves, i.e. modes of collectively precessing spins. Thermally excited magnons in thin magnetic films generate stray fields at the film surface which can be detected using nitrogen-vacancy (NV) centers. NVs are lattice defects in diamond and are able to couple with magnon stray fields. Assuming a thermal occupancy of magnon modes, we study the magnetization dynamics of magnons propagating through thin magnetic insulators using the Landau-Lifshitz-Gilbert equation. We implement a numerical model to predict and understand the response of the NV center to proximal magnons in thin films. We investigate how the NV relaxation rate changes for different NV orientations by extending and generalizing the existing theory on chiral magnetic noise, and simulate an experimental setup for an NV placed just above the surface of a thin magnetic insulator. The simulation includes a static bias field in an arbitrary orientation with respect to the quantization axis of the NV center using the diamond's tetrahedral symmetry. This extended model is in demand due to limitations in present-day measurement techniques to align the bias field with an NV center. We use it to detect magnons that contribute to the relaxation rate of the NV, and determine an NV-to-film distance of 0.28(3) μm, from measured relaxation rates of an NV center placed above an yttrium-iron-garnet film with a thickness of 235(10) nm. Our model is available as an open-source Python module.