In order to better characterize the rich supernova remnant (SNR) population of M83 (NGC 5236), we have obtained high-resolution (~85km/s) spectra of 119 of the SNRs and SNR candidates in M83 with Gemini/GMOS, as well as new spectra of the young SNRs B12-174a and SN1957D. Most of the SNRs and SNR candidates have [SII]:H{alpha} ratios that exceed 0.4. Combining these results with earlier studies we have carried out with MUSE and at lower spectroscopic resolution with GMOS, we have confirmed a total of 238 emission nebulae to be SNRs on the basis of their [SII]:H{alpha} ratios, about half of which have emission lines that show velocity broadening greater than 100km/s, providing a kinematic confirmation that they are SNRs and not HII regions. Looking at the entire sample, we find a strong correlation between velocity widths and the line ratios of [OI]{lambda}6300:H{alpha}, [NII]{lambda}6584:H{alpha}, and [SII]{lambda}{lambda}6716,6731:H{alpha}. The density-sensitive [SII]{lambda}6716:{lambda}6731 line ratio is strongly correlated with SNR diameter, but not with the velocity width. We discuss these results in the context of previously published shock models.