Goos-Hänchen (GH) shifts are theoretically investigated in parity-time ($\mathcal{PT}$)-symmetric photonic crystals with a Weyl semimetal (WSM) defect layer at the center. The transmission spectrum features a sharp Fano resonance coupled with a laser point, both originating from the epsilon near zero response. Remarkably, giant quasireciprocal GH shifts up to $3.28\times {10}^4\lambda$ are achieved at the Fano resonance frequency, despite the system's overall nonreciprocal reflectance characteristics. The coincidence of the Fano resonance and laser point makes the corresponding reflectance of the GH shift high enough to be detected. These GH shifts demonstrate strong dependence on incidence angle (θ) and gain-loss factor ($q$) while maintaining a fixed operational wavelength. Notably, abrupt negative-to-positive inversions of the GH shifts occur at critical values of θ and $q$, with a small distinct nonreciprocal regime. The GH shifts can be further tuned by increasing the WSM's Fermi energy ($E_f$), enhancing both the GH shift magnitude and its operational frequency. Elevating temperatures ($T$) reduce the shift magnitude and induce a blueshift. Additionally, these phenomena are unique to the two-Weyl-node configuration—no comparable Fano resonance or GH shifts appear for systems with additional Weyl nodes. The exceptional sensitivities of these GH shifts to θ, $q, E_f$, and $T$ suggest promising applications in optical switching, precision sensing, and quasireciprocal photonic devices.

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• Nonlinear optics