Industrial hemp is characterized by a huge amount of by-products, such as inflorescences, that may represent high-quality sources of biomolecules with pharmaceutical interest. In the present study, we have evaluated the phytochemical profile, including terpene and terpenophenolic compounds, of the essential oils (EOs) of Futura 75, Carmagnola selezionata and Eletta campana hemp varieties. The EOs were also tested for antifungal properties toward Trichophyton mentagrophytes, Trichophyton rubrum, Arthroderma crocatum, Arthroderma quadrifidum, Arthroderma gypseum, Arthroderma curreyi, and Arthroderma insingulare. In parallel, we investigated the inhibitory effects of the EOs against tyrosinase, and the production of prostaglandin E2 in isolated mouse skin exposed to hydrogen peroxide. In human H1299 lung adenocarcinoma cells, we also evaluated the influence of the EOs on the gene expression of angiotensin-converting enzyme 2 (ACE2) and transmembrane protease serine 2 (TMPRSS2), which are involved in SARS-CoV-2 entry in human host. E-caryophyllene and α-pinene were the prominent terpenes in the EOs, whereas the cannabidiolic acid was the terpenophenol present at higher concentration. The EOs inhibited the growth of all tested dermatophytes species. In isolated skin specimens, EOs prevented the hydrogen-peroxide-induced synthesis of prostaglandin E2, consistent with the intrinsic antityrosinase activity. Finally, in H1299 cells, all tested EOs reduced the gene expression of ACE-2 and TMPRSS2, as well. Therefore, the present findings highlight the rationale for the use of the present EOs against infectious diseases.