The performance of mid-infrared (MIR) on-chip gas sensors, operating via laser absorption spectroscopy, hinges critically on light-matter interaction dynamics, significantly influenced by external confinement and the effective light path length. Conventional on-chip sensors, however, face challenges in achieving the required limit of detection for highly sensitive applications, primarily due to their intrinsically short effective light path. Furthermore, these sensors are limited in their spectral range coverage within the MIR spectrum by the constraints of standard silicon-based platforms. To overcome these limitations, our research presents a novel approach to fabricate a freestanding germanium (Ge) photonic crystal waveguide (PCW) on a germanium-on-insulator (Ge-OI) platform, utilizing yttrium oxide (Y2O3) as the buried oxide layer. This device leverages the broad transparent windows of Ge and Y2O3, broadening the spectral coverage across the MIR range. The introduction of the PCW and its slow light effect significantly elevate external confinement and light-matter interactions, enabling a notable reduction in waveguide length, which traditionally limits on-chip configurations. The freestanding structure not only expands the sensing region and enhances external confinement but also prevents the emergence of leaky modes within the PCW. As a result, our compact sensor achieves an exceptionally low LoD of 7.56 ppm for carbon dioxide (CO2) sensing at the operational wavelength of 4.23 μm, with a compact waveguide length of only 800 μm.