Essential oils (EOs) are mixtures of volatile plant secondary metabolites and have been exploited by humans for thousands of years for various purposes because of their many bioactivities. In this study, the EO from Thymus capitatus, a thyme species organically cultured on the Greek Island of Lemnos, was analyzed for its chemical composition (through GC-FID and GC-MS), antioxidant activity (AA), and total phenolic content (TPC), as well as its antimicrobial and antibiofilm actions against three important foodborne bacterial pathogens (Salmonella enterica ser. Typhimurium, Listeria monocytogenes, and Yersinia enterocolitica). For the latter investigations, the minimum inhibitory concentrations (MICs) and minimum biofilm inhibitory concentrations (MBICs) of the EO against the planktonic and biofilm growth of each pathogen were determined, together with the minimum biofilm eradication concentrations (MBECs). Results revealed that T. capitatus EO was rich in thymol, p-cymene, and carvacrol, presenting high AA and TPC (144.66 μmol TroloxTM equivalents and 231.32 mg gallic acid equivalents per g of EO, respectively), while its MICs and MBICs ranged from 0.03% to 0.06% v/v and 0.03% to 0.13% v/v, respectively, depending on the target pathogen. The EO was able to fully destroy preformed (mature) biofilms of all three pathogenic species upon application for 15 min, with MBECs ranging from 2.00 to 6.25% v/v. Overall, the results demonstrate that the EO of organically cultured T. capitatus presents strong antioxidant, antibacterial, and antibiofilm properties and could, therefore, be further exploited as a functional and antimicrobial natural formulation for food and health applications.