Metal-enhanced fluorescence (MEF) has found widespread application in biomedical sensing and in vivo tissue imaging systems. To enhance MEF efficiency, it is necessary to optimize the interaction between metal nanoparticle plasmon and the fluorophore molecule. The size and shape of the nanoparticle, the nanoscale gap between the fluorescent molecule and the nanoparticle, and the excitation wavelength are critical parameters. In this study, we propose a model for a more complete and accurate description of the processes of molecular excitation and generation of the fluorescence spectral response, introducing new concept of effective properties for field enhancement factor, quantum yield, and fluorescence enhancement factor. The influence of the spectral properties of both the nanostructure plasmon and the fluorophore molecule on the optimal tuning of fluorescent complexes is studied. Particular attention is paid to the analysis of the spectral properties of plasmon resonance and calculations of the near-field intensity enhancement of the plasmonic nanostructure's excitation field. Numerical results for optimizing the MEF of fluorescent complexes based on TagRFP and gold (silver) nanorods composites are presented. The advantages of the proposed model for the optimal design of new nanomaterials with unique fluorescent properties are discussed.