Tomato spotted wilt virus (TSWV; genus Orthotospovirus, family Tospoviridae) has a huge impact on a large range of plants worldwide. In this study, we determined the sequence of the large (L) RNA segment that encodes the RNA-dependent RNA polymerase (RdRp) from a TSWV isolate (LYE51) collected in the south of France. Analysis of the phylogenetic relationships of TSWV-LYE51 with other TSWV isolates shows that it is closely related to other European isolates. A 3D model of TSWV-LYE51 RdRp was built by homology with the RdRp structure of the La Crosse virus (genus Orthobunyavirus, family Peribunyaviridae). Finally, an analysis of positive and negative selection was carried out on 30 TSWV full-length RNA L sequences and compared with the phylogeny and the protein structure data. We showed that the seven codons that are under positive selection are distributed all along the RdRp gene. By contrast, the codons associated with negative selection are especially concentrated in three highly constrained domains: the endonuclease in charge of the cap-snatching mechanism, the thumb domain and the mid domain. Those three domains could constitute good candidates to look for host targets on which genetic resistance by loss of susceptibility could be developed.