In this paper, we present a simple approach to study the coupling mechanisms between a plasmonic system consisting of bowtie nanoantennas and a photonic structure based on a Fabry-Perot interferometer. The nanoantenna array is represented by an equivalent homogeneous layer placed at the interferometer surface and yielding the effective dielectric function of the NA resonance. A phase matching model based on thin film interference is developed to describe the multi-layer interferences in the device and to analyze the fringe variations induced by the introduction of the plasmonic layer. The general model is validated by an experimental system consisting of a bowtie nanoantenna array and a porous-silicon-based interferometer. The optical response of this hybrid device exhibits both the enhancement induced by the nanoantenna resonance and the fringe pattern of the interferometer. Using the phase matching model, we demonstrate that strong coupling can occur in such a system, leading to fringe splitting. A study of the splitting strength and of the coupling behavior is given. The model study performed in this work enables to gain deeper understanding of the optical behavior of plasmonic/photonic hybrid devices.