Since their experimental discovery in 2015, Weyl semimetals generated a large amount of attention due their intriguing physical properties that arise from their linear electron dispersion relation and topological surface states. In particular in the field of nonlinear (NL) optics and light harvesting, Weyl semimetals have shown outstanding performances and achieved record NL conversion coefficients. In this context, we perform first steps towards Weyl semimetal nanophotonics by thoroughly characterizing the linear and NL optical behavior of epitaxially grown niobium phosphide (NbP) thin films, covering the visible to near-infrared regime of the electromagnetic spectrum. Despite the measured high linear absorption, third-harmonic generation studies demonstrate high conversion efficiencies up to 10-4%, that can be attributed to the topological electron states at the surface of the material. Furthermore, nondegenerate pump-probe measurements with sub-10 fs pulses reveal a maximum modulation depth of about 1%, completely decaying within 100 fs and therefore suggesting the possibility of developing devices based on NbP with all-optical switching bandwidths of up to 10 THz. Altogether, our work reveals promising NL optical properties of Weyl semimetal thin films that are outperforming bulk crystals of the same material, laying the grounds for nanoscale applications, enabled by top-down nanostructuring, such as light-harvesting, on-chip frequency conversion and all-optical processing.