Surface plasmonic sensors have received considerable attention, found extensive applications, and outperformed conventional optical sensors. In this work, biopolymer chitosan (CS) was used to prepare the bilayer structure (CS/Au) of a plasmonic refractive index sensor for dopamine (DA) detection. The sensing characteristics of the developed plasmonic sensor were evaluated. Increasing DA concentrations significantly shifted the SPR dips. The sensor exhibited stability and a refractive index sensitivity of 8.850°/RIU in the linear range 0.1 nM to 1 µM with a detection limit of 0.007 nM and affinity constant of 1.383 × 108 M−1. The refractive index and thickness of the CS/Au structure were measured simultaneously by fitting the obtained experimental findings to theoretical data based on Fresnel equations. The fitting yielded the refractive index values n (1.5350 ± 0.0001) and k (0.0150 ± 0.0001) for the CS layer contacting 0.1 nM of DA, and the thickness, d was (15.00 ± 0.01) nm. Then, both n and d values increased by increasing DA concentrations. In addition, the changes in the FTIR spectrum and the variations in sensor surface roughness and structure obtained by AFM analysis confirmed DA adsorption on the sensing layer. Based on these observations, CS/Au bilayer has enhanced the performance of this plasmonic sensor, which showed promising importance as a simple, low-cost, and reliable platform for DA sensing.