  We report on low-frequency current fluctuations, i.e. electronic noise, in
quasi-one-dimensional (TaSe$_4$)$_2$I Weyl semimetal nanoribbons. It was found
that the noise spectral density is of the 1/f type and scales with the square
of the current, S~I^2 (f is the frequency). The noise spectral density
increases by almost an order of magnitude and develops Lorentzian features near
the temperature T~225 K. These spectral changes were attributed to the
charge-density-wave phase transition even though the temperature of the noise
maximum deviates from the reported Peierls transition temperature in bulk
(TaSe$_4$)$_2$I crystals. The noise level, normalized by the channel area, in
these Weyl semimetal nanoribbons was surprisingly low, $\sim 10^{-9}$
um$^2$Hz$^{-1}$ at f=10 Hz, when measured below and above the Peierls
transition temperature. Obtained results shed light on the specifics of
electron transport in quasi-1D topological Weyl semimetals and can be important
for their proposed applications as downscaled interconnects.
