Accumulating evidence suggests that inherited melanoma is not rare and approx. one in seven individuals with melanoma has clinically relevant hereditable cancer-predisposing and/or -susceptibility variant(s). Concerning its germline genetic background, genetic screening aims to identify either variants of predisposing genes with high penetrance or variants of susceptibility genes with medium or low penetrance. However, less attention is paid to genetic testing of germline variants of genes influencing patients’ survival outcomes or enhancing the design of new therapies. We aimed to investigate whether the germline genetic background of a Hungarian melanoma cohort (n = 17) contains any pathogenic or likely pathogenic variants of the BRCA2, POLE, WRN, FANCI, PALB2, and RAD54B genes and if the presence of these variants correlate with the clinical findings of the patients, including the advanced stage of melanoma, poor prognosis, and poor survival. We identified three novel variants in the FANCI gene and one novel variant in the RAD54B gene. We detected rapid disease progression, unfavorable outcome, and therapeutic resistance in the patient carrying the likely pathogenic FANCI variant. Our study highlights the importance of screening germline variants of genes influencing melanoma progression, therapy resistance, and survival of patients.