Nonlinear optical and structural properties of tungsten-doped, amorphous-carbon films were studied with optical second harmonic generation (SHG), scanning tunnelling microscopy (STM) and atomic-force microscopy (AFM) in a wide range of tungsten concentrations. The dependence of SHG intensity on the film resistivity R reveals a sharp increase of more than an order of magnitude at R less than or similar to 3x10(-4) Omega cm. This increase in nonlinear susceptibility can be attributed to an insulator-to-metal phase transition and the appearance of metallic conductivity in highly doped films. A violation of the polarization selection rules for reflected SHG was observed. The isotropic s-polarized SHG is coming from nm-scale roughness of the film surface, which is consistent with the results of STM/AFM measurements.