Semiconducting nanoplatelets (NPLs) have attracted great attention due to the superior photophysical properties compared to their quantum dot analogs. Understanding and tuning the optical and electronic properties of NPLs in a plasmonic environment is a new paradigm in the field of optoelectronics. Here, we report on the resonant plasmon enhancement of light emission including Raman scattering and photoluminescence from colloidal CdSe/CdS nanoplatelets deposited on arrays of Au nanodisks fabricated by electron beam lithography. The localized surface plasmon resonance (LSPR) of the Au nanodisk arrays can be tuned by varying the diameter of the disks. In the case of surface-enhanced Raman scattering (SERS), the Raman intensity profile follows a symmetric Gaussian shape matching the LSPR of the Au nanodisk arrays. The surface-enhanced photoluminescence (SEPL) profile of NPLs, however, follows an asymmetric Gaussian distribution highlighting a compromise between the excitation and emission enhancement mechanisms originating from energy transfer and Purcell effects. The SERS and SEPL enhancement factors depend on the nanodisk size and reach maximal values at 75 and 7, respectively, for the sizes, for which the LSPR energy of Au nanodisks coincides with interband transition energies in the semiconductor platelets. Finally, to explain the origin of the resonant enhancement behavior of SERS and SEPL, we apply a numerical simulation to calculate plasmon energies in Au nanodisk arrays and emission spectra from NPLs in such a plasmonic environment.