We present a theoretical approach to narrow the plasmon linewidth and enhance the near-field intensity at a plasmonic dimer gap (hot spot) through coupling the electric localized surface plasmon (LSP) resonance of a silver hemispherical dimer with the resonant modes of a Fabry-Perot (FP) cavity. The strong coupling is demonstrated by the large anticrossing in the reflection spectra and a Rabi splitting of 76 meV. Up to 2-fold enhancement increase can be achieved compared to that without using the cavity. Such high field enhancement has potential applications in optics, including sensors and high resolution imaging devices. In addition, the resonance splitting allows for greater flexibility in using the same array at different wavelengths. We then further propose a practical design to realize such a device and include dimers of different shapes and materials.