Nanocarbon-based vapour sensors are increasingly used to make anticipated diagnosis of diseases by the analysis of volatile organic compound (VOC) biomarkers from the breath, i.e., volatolomics. However, given the tiny number of molecules to detect, usually only tens of parts per billion (ppb), increasing the sensitivity of polymer nanocomposite chemoresistive transducers is still a challenge. As the ability of these nanosensors to convert the interactions with chemical compounds into changes of resistance, depends on the variations of electronic transport through the percolated network of the conducting nanofillers, it is a key parameter to control. Actually, in this conducting architecture, the bottlenecks for electrons’ circulation are the interparticular junctions giving either ohmic conduction in the case of close contacts or quantum tunnelling when jumps though gaps are necessary. This in turn depends on a number of nanometric parameters such as the size and geometry of the nanofillers (spherical, cylindrical, lamellar), the method of structuring of the conductive architecture in the sensory system, etc. The present study focuses on the control of the interparticular junctions in quantum-resistive vapour sensors (vQRS) by nanoassembling pristine CNT or graphene covalently or noncovalently functionalized with spherical Buckminster fullerene (C60) into a percolated network with a hybrid structure. It is found that this strategy allows us to significantly boost, both selectivity and sensitivity of pristine CNT or graphene-based transducers exposed to a set of seven biomarkers, ethanol, methanol, acetone, chloroform, benzene, toluene, cyclohexane and water. This is assumed to result from the spherical fullerene acting on the electronic transport properties at the nanojunctions between the CNT or graphene nanofillers.