The low temperature reaction between CN and benzene (C$_6$H$_6$) is of significant interest in the astrochemical community due to the recent detection of benzonitrile, the first aromatic molecule identified in the interstellar medium (ISM) using radio astronomy. Benzonitrile is suggested to be a low temperature proxy for benzene, one of the simplest aromatic molecules, which may be a precursor to polycyclic aromatic hydrocarbons (PAHs). In order to assess the robustness of benzonitrile as a proxy for benzene, low temperature kinetics measurements are required to confirm whether the reaction remains rapid at the low gas temperatures found in cold dense clouds. Here, we study the C$_6$H$_6$ + CN reaction in the temperature range 15--295 K, using the well-established CRESU technique (a French acronym standing for Reaction Kinetics in Uniform Supersonic Flow) combined with Pulsed Laser Photolysis-Laser-Induced Fluorescence (PLP-LIF). We obtain rate coefficients, $k(T)$, in the range (3.6--5.4) $times$ 10$^{-10}$ cm$^3$ s$^{-1}$ with no obvious temperature dependence between 15--295 K, confirming that the CN + C$_6$H$_6$ reaction remains rapid at temperatures relevant to the cold ISM.