In this report, the electrical properties of plasma polymer films functionalized with ZnO nanoparticles were investigated with respect to their potential applications in biomaterials and microelectronics fields. The nanocomposite films were produced using a single-step method that combines simultaneous plasma polymerization of renewable geranium essential oil with thermal decomposition of zinc acetylacetonate Zn(acac)2. The input power used for the deposition of composites were 10 W and 50 W, and the resulting composite structures were abbreviated as Zn/Ge 10 W and Zn/Ge 50 W, respectively. The electrical properties of pristine polymers and Zn/polymer composite films were studied in metal–insulator–metal structures. At a quantity of ZnO of around ~1%, it was found that ZnO had a small influence on the capacitance and dielectric constants of thus-fabricated films. The dielectric constant of films with smaller-sized nanoparticles exhibited the highest value, whereas, with the increase in ZnO particle size, the dielectric constant decreases. The conductivity of the composites was calculated to be in the in the range of 10−14–10−15 Ω−1 m−1, significantly greater than that for the pristine polymer, the latter estimated to be in the range of 10−16–10−17 Ω−1 m−1.