Superoxide dismutase 1 (SOD1) is one of the causative genes associated with amyotrophic lateral sclerosis (ALS), a neurodegenerative disorder. SOD1 aggregation contributes to ALS pathogenesis. A fraction of the protein is localized in the nucleus (nSOD1), where it seems to be involved in the regulation of genes participating in the oxidative stress response and DNA repair. Peripheral blood mononuclear cells (PBMCs) were collected from sporadic ALS (sALS) patients (n = 18) and healthy controls (n = 12) to perform RNA-sequencing experiments and differential expression analysis. Patients were stratified into groups with “high” and “low” levels of nSOD1. We obtained different gene expression patterns for high- and low-nSOD1 patients. Differentially expressed genes in high nSOD1 form a cluster similar to controls compared to the low-nSOD1 group. The pathways activated in high-nSOD1 patients are related to the upregulation of HSP70 molecular chaperones. We demonstrated that, in this condition, the DNA damage is reduced, even under oxidative stress conditions. Our findings highlight the importance of the nuclear localization of SOD1 as a protective mechanism in sALS patients.