Plasmon-enhanced Förster resonance energy transfer (FRET) in donor-acceptor pairs with different energy transfer efficiency was studied. For this purpose layered films of dyes were prepared by using of Langmuir-Blodgett technology on the surface of silver island films. It was shown that the maximum of the plasmon effect on the fluorescence intensity of the dye film is observed at a distance of ~6 nm from the island silver film. The plasmon effect of enhancing energy transfer efficiency (EET) is greater for a pair with low value of EET. In this case, the rate constant of FRET near the silver film was almost 4 times faster for the Fluorescein–Nile red pair, compared to the pair of Rhodamine B-Nile red. The results can be used for increasing the photosensitivity of solar cells in the visible region of the spectrum, in studying of photobiological processes associated with the collection and delivery of light energy to the reaction centers, as well as to create materials with desired properties, sensors and light energy converters.