We report on a flow-through optical sensor consisting of a microcapillary with mirrored channels. Illuminating the structure from the side results in a complicated spectral interference pattern due to the different cavities formed between the inner and outer capillary walls. Using a Fourier transform technique to isolate the desired channel modes and measure their resonance shift, we obtain a refractometric detection limit of (6.3 ± 1.1) x 10-6 RIU near a center wavelength of 600 nm. This simple device demonstrates experimental refractometric sensitivities up to (5.6 ± 0.2) x 102 nm/RIU in the visible spectrum, and it is calculated to reach 1540 nm/RIU with a detection limit of 2.3 x 10-6 RIU at a wavelength of 1.55 µm. These values are comparable to or exceed some of the best Fabry-Perot sensors reported to date. Furthermore, the device can function as a gas or liquid sensor or even as a pressure sensor owing to its high refractometric sensitivity and simple operation.