The interaction effect of the fundamental mode in a special photonic crystal fiber (PCF) with a thin-film absorbing coating deposited on a surface of a fiber cladding on the optical transmission of the PCF is theoretically studied. It is shown that the transmission has a multi-peak spectrum that is determined by the resonance capture of the fundamental PCF mode energy by the coating. In some cases, this capture is explained by a resonance coupling between the fundamental core mode and leaky modes of the coating, or between the fundamental PCF mode and cladding modes located between PCF air channels and the coating. Examples are presented of using this effect to develop fiber-optic sensors of refractive index or pressure, and to sense a nanoscale adsorption layer of ammonia molecules deposited on a coating surface contacting air.