Metal-enhanced fluorescence (MEF), resulting from the near-field interaction of fluorophores with metallic nanostructures, has emerged as a powerful tool for dramatically improving the performance of fluorescence-based biomedical applications. Allowing for lower autofluorescence and minimal photoinduced damage, the development of multifunctional and multiplexed MEF platforms in the near-infrared (NIR) windows is particularly desirable. Here, a low-cost fabrication method based on nanosphere lithography is applied to produce tunable three-dimensional (3D) gold (Au) nanohole–disc arrays (Au-NHDAs). The arrays consist of nanoscale glass pillars atop nanoholes in a Au thin film: the top surfaces of the pillars are Au-covered (effectively nanodiscs), and small Au nanoparticles (nanodots) are located on the sidewalls of the pillars. This 3D hole–disc (and possibly nanodot) construct is critical to the properties of the device. The versatility of our approach is illustrated through the production of uniform and highly reproducible Au-NHDAs with controlled structural properties and tunable optical features in the NIR windows. Au-NHDAs allow for a very large NIR fluorescence enhancement (more than 400 times), which is attributed to the 3D plasmonic structure of the arrays that allows strong surface plasmon polariton and localized surface plasmon resonance coupling through glass nanogaps. By considering arrays with the same resonance peak and the same nanodisc separation distance, we show that the enhancement factor varies with nanodisc diameter. Using computational electromagnetic modeling, the electric field enhancement at 790 nm was calculated to provide insights into excitation enhancement, which occurs due to an increase in the intensity of the electric field. Fluorescence lifetime measurements indicate that the total fluorescence enhancement may depend on controlling excitation enhancement and therefore the array morphology. Our findings provide important insights into the mechanism of MEF from 3D plasmonic arrays and establish a low-cost versatile approach that could pave the way for novel NIR-MEF bioapplications.