Exhaled human breath contains a mixture of gases including nitrogen, oxygen, carbon dioxide, water vapour and low molecular weight volatile organic compounds (VOCs). Different VOCs detected in human breath condensate have been recently related to several metabolic processes occurring inside body tissues in the pathological state, as candidate biomarkers for monitoring conditions such as lung injury, airway inflammation, immunity dysfunction, infection, and cancer. Current techniques for detecting these compounds include several types of mass spectroscopy, which are highly costly, time-consuming and dependent on trained personnel for sample analysis. The need for fast and label-free biosensors is paving the way towards the design of novel and portable electronic devices for point-of-care diagnosis with VOCs such as E-noses, and based on the measurement of signal signatures derived from their chemical composition. In this paper, we propose a device for VOC detection that was tested inside a controlled gas flow setup, resorting to graphene field-effect transistors (GFETs). Electrical measurements from graphene directly exposed to nitrogen plus VOC vapours involved cyclic measurements for the variation of graphene's resistance and low-frequency spectral noise in order to obtain distinctive signatures of the tested compounds in the time and frequency domains related, respectively, to Gutmann's theory for donor-acceptor chemical species and spectral sub-band analysis.