The reported chalcogenide (ChG) rectangular waveguide sensors with a small evanescent field need a large waveguide length to obtain an enhanced light-gas interaction effect. To make such sensors compact and improve the light-gas interaction effect, a microcavity-enhanced absorption spectroscopy technique for methane (CH4) detection was proposed using a mid-infrared chalcogenide/silica-on-fluoride horizontal slot-waveguide racetrack resonator. For the horizontal slot waveguide, an equivalent sensor model (ESM) and related formulations were proposed to simplify the analysis of the racetrack resonator sensor model (RRSM), and the ESM was verified through a comparison between the theoretical result of ESM and the simulation result of RRSM based on the finite element method (FEM). Due to the use of a chalcogenide/silica-on-fluoride horizontal slot-waveguide structure, the waveguide parameters were optimized to obtain a high power confinement factor of 44.63% at the wavelength of 3291 nm, which is at least 5 times higher than other ChG rectangular waveguides. The waveguide length is reduced at least 30 times due to the use of the optimized chalcogenide/silica-on-fluoride horizontal slot-waveguide and racetrack resonator. The limit of detection (LoD) is 3.87 ppm with an intrinsic waveguide loss of 3 dB/cm and an amplitude coupling ratio of 0.1 for the resonator. The response time is less than 5 µs due to the small light-gas interaction area. The influences of environmental pressure and waveguide intrinsic loss on the sensing characteristics were discussed. The compact racetrack resonator sensor structure and equivalent analytical model can also be adopted in the design of an on-chip waveguide sensor for the detection of other gas species.