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In this letter, we demonstrate low-frequency noise (LFN) characterization of an InAs vertical gate-all-around hafnium-zirconium oxide (HZO) ferroelectric field-effect transistor (FeFET). The LFN characteristics are investigated before and after ferroelectric switching for up to 1000 cycles in the FeFET. The evolution of such cycling reveals distinct differences in the LFN for the two polarization states. The LFN is found to change more during cycling in the high-VT state than in the low-VT state, where the latter has an increased LFN already at various current levels during the first switching cycle. Our findings indicate that the mobility fluctuation and carrier number fluctuation are the dominant source of the LFN for low currents in the off-state and near-VT current levels, respectively, verified by fitting the experimental data to the different models