The transmission of light through metallic films with periodic double nanoholes is studied using vectorial three-dimensional finite element method. Special emphasis is given on understanding different transmission resonances arising in gold and silver films with periodic sub-wavelength holes of different shapes. The spectral shift of the hole-shape resonance resulting from a variation of the hole refractive index is analyzed for a double nanohole geometry in the transmission mode using numerical simulations. Specifically, the role of field enhancement at the apexes of the double nanohole in the sensing of medium within the hole cavity is pointed out and discussed. The presence of sharp apexes within the double nanoholes significantly improves the resonance sensitivity as compared to rectangular holes of comparable area. Impact of possible manufacturing errors on the overall sensitivity is also characterized. Robustness and a relatively simple fabrication procedure make these kinds of refractive index sensors practically attractive.