We analyzed the resonant coupling in the low-refractive-index sensor based on a directional coupler implemented in a microstructured optical fiber with a composite core and the parallel analyte channel in the form of a hollow-core waveguide. We showed the possibility of an 8-fold increase in the analyte channel radius that is equivalent to a 64-fold increase in its cross section, in comparison to the existing design. With an increase in the analyte channel radius, the resonance frequencies of the composite core mode and the satellite waveguide modes shift to longer wavelengths, while the dispersion curves of the high-order modes of the satellite waveguide tend to merge and their resonances become less pronounced than the resonances of the low-order modes. With an increase in the analyte channel radius from 2 to , the sensor sensitivity increases by 40% and the detection limit becomes lower by a factor of 2. Such an increase in the analyte channel radius also eliminates the need in a high-pressure pump for filling the channel with analyte and thus makes this sensor much more practical than was previously thought.