We present optical and near-infrared (NIR) imaging data of the radio-loud, narrow-line Seyfert 1 galaxy 1H 0323+342, which shows intense and variable gamma-ray activity discovered by the Fermi satellite with the Large Area Telescope. Near-infrared and optical images are used to investigate the structural properties of the host galaxy of 1H 0323+342; this together with optical spectroscopy allows us to examine its black hole mass. Based on two-dimensional (2D) multiwavelength surface-brightness modeling, we find that statistically, the best model fit is a combination of a nuclear component and a Sersic profile (n~2.8). However, the presence of a disk component (with a small bulge n~1.2) also remains a possibility and cannot be ruled out with the present data. Although at first glance a spiral-arm-like structure is revealed in our images, a 2D Fourier analysis of the imagery suggests that this structure corresponds to an asymmetric ring, likely associated with a recent violent dynamical interaction. We discuss our results in the context of relativistic jet production and galaxy evolution.