The low-frequency noise is of special interest for carbon nanotubes devices, which are building blocks for a variety of sensors, including radio frequency and terahertz detectors. We studied noise in as-fabricated and aged carbon nanotube networks (CNNs) field-effect transistors. Contrary to the majority of previous publications, as-fabricated devices demonstrated the superposition of generation-recombination (GR) and 1/f noise spectra at a low-frequency range. Although all the devices revealed identical current-voltage characteristics, GR noise was different for different transistors. This effect is explained by the different properties and concentrations of trap levels responsible for the noise. Unexpectedly, exposure of these devices to the atmosphere reduced both the resistance and GR noise due to nanotube's p-doping by adsorbed water molecules from the ambient atmosphere. The presence of the generation recombination noise and its dependences on the environment provides the basis for selective gas sensing based on the noise measurements. Our study reveals the noise properties of CNNs that need to be considered when developing carbon nanotubes-based selective gas sensors.