Plasmonic field enhancement localized around metallic particles is useful for improving sensitivity in sensing applications. In this research, we used finite-difference time-domain modelling to study plasmonic field enhancement in an array of polystyrene particles covered with gold, to understand the effect of the incident polarization and the particle shape. The gold particle shapes were changed from a perfect sphere to an ellipsoid with the vertical height varying as 930 nm, 880 nm and 830 nm, while the horizontal diameter was fixed at 930 nm. The simulated structure was composed of gold spheres arranged in a hexagonal-close-packed array on an 80-nm thick gold film. When the metallic spheres were arranged on the gold film the plasmonic enhancement was up to 1.8 times greater than for the array without a metallic film. The plasmon resonances of the array were strongest at the bridge connections between the particles, and at the surface of the particles without connections. Where there were no particle-particle connections, the resonant field distributions had one, two, three and higher nodes. In addition, the absorption spectra for various sized rectangular structures with gold particles at the center were investigated to determine the effect of the lattice period on the wavelengths of resonance. The results showed that the lattice period did not greatly perturb the resonance modes for this structure. This study aids improved design of plasmonic-photonic crystals with micron-scale periods for sensing applications.