Phase transitions and critical phenomena, which are dominated by fluctuations and correlations, are one of the fields replete with physical paradigms and unexpected discoveries. Especially for two-dimensional magnetism, the limitation of the Ginzburg criterion leads to enhanced fluctuations breaking down the mean-field theory near a critical point. Here, by means of magnetic resonance, we investigate the behavior of critical fluctuations in the two-dimensional ferromagnetic insulators $rm CrXTe_3 (X=Si, Ge)$. After deriving the classical and quantum models of magnetic resonance, we deem the dramatic anisotropic shift of the measured $g$ factor to originate from fluctuations with anisotropic interactions. The deduction of the $g$ factor behind the fluctuations is consistent with the spin-only state (${gapprox}$ 2.050(10) for $rm CrSiTe_3$ and 2.039(10) for $rm CrGeTe_3$). Furthermore, the abnormal enhancement of $g$ shift, supplemented by specific heat and magnetometry measurements, suggests that $rm CrSiTe_3$ exhibits a more typical two-dimensional nature than $rm CrGeTe_3$ and may be closer to the quantum critical point.
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