In this communication, we systematically investigate the effects of Fano-type coupling between long-range photonic resonances and localized surface plasmons on the second harmonic generation from periodic arrays of Au nanoparticles arranged in monomer and dimer geometries. Specifically, by scanning the wavelength of an ultrafast tunable pump laser over a large range, we measure the second harmonic excitation spectra of these arrays and demonstrate their tunability with particle size and separation. Moreover, through a comparison with linear optical transmission spectra, which feature asymmetric Fano-type lineshapes, we demonstrate that the second harmonic generation is enhanced when coupled photonic-plasmonic resonances of the arrays are excited at the fundamental pump wavelength, thus boosting the intensity of the electromagnetic near-fields. Our experimental results, which are supported by numerical simulations of linear optical transmission and near-field enhancement spectra based on the Finite Difference Time Domain method, demonstrate a direct correlation between the onset of Fano-type coupling and the enhancement of second harmonic generation in arrays of Au nanoparticles. Our findings enable the engineering of the nonlinear optical response of Fano-type coupled nanoparticle arrays that are relevant to a number of device applications in nonlinear nano-optics and plasmonics, such as on-chip frequency generators, modulators, switchers, and sensors.