Fractal shaped periodic nanostructures formed with a $100\mathrm{nm}$ period square lattice of gold nanoparticles placed on a gold film are characterized using far-field nonlinear scanning optical microscopy, in which two-photon photoluminescence (TPL) excited with a strongly focused femtosecond laser beam (in the wavelength range of $730–790\mathrm{nm}$ ) is detected. TPL images obtained for all wavelengths in the laser range feature diffraction-limited $(\sim 0.6\mu \mathrm{m})$ bright spots corresponding to intensity enhancements of up to $\sim 170$ , whose positions are dictated by the incident light wavelength and polarization. We relate the observed TPL enhancements to constructive interference of surface plasmon polaritons partially reflected inside the structure boundaries and support the analysis with numerical simulations using the Green dyadic field propagator.