Drug resistance is rising to alarming levels, constituting one of the major threats to global health. The overexpression of efflux pumps and the formation of biofilms constitute two of the most common resistance mechanisms, favoring the virulence of bacteria. Therefore, the research and development of effective antimicrobial agents that can also counteract resistance mechanisms are extremely important. Pyrazino[2,1-b]quinazoline-3,6-diones, from marine and terrestrial organisms and simpler synthetic analogues, were recently disclosed by us as having relevant antimicrobial properties. In this study, using a multi-step approach, it was possible to synthesize new pyrazino[2,1-b]quinazoline-3,6-diones focusing on compounds with fluorine substituents since, to the best of our knowledge, the synthesis of fluorinated fumiquinazoline derivatives had not been attempted before. The new synthesized derivatives were screened for antibacterial activity and, along with previously synthetized pyrazino[2,1-b]quinazoline-3,6-diones, were characterized for their antibiofilm and efflux-pump-inhibiting effects against representative bacterial species and relevant resistant clinical strains. Several compounds showed relevant antibacterial activity against the tested Gram-positive bacterial species with MIC values in the range of 12.5–77 μM. Furthermore, some derivatives showed promising results as antibiofilm agents in a crystal violet assay. The results of the ethidium bromide accumulation assay suggested that some compounds could potentially inhibit bacterial efflux pumps.