European eel (Anguilla anguilla) elvers (initial body weight (BW) = 3 g) were raised in triplicate for 60 days in a biofloc system (BFT) at 21 °C. Data from the current first study evaluating this farming technology indicated that European eel elvers adapted well to BFT systems as data on growth performance (specific growth rate = 1.48% ± 0.13 BW/day and FCR = 1.05 ± 0.09) indicated, with production costs using BFT being lower than conventional RAS units. The most critical issues associated with this aquaculture system were the maintenance of the biofloc in tanks by the regular addition of refined sugar (46% C) to keep a relationship for C:N of 20:1, and the prevention of emergence of opportunistic pathogens like the monogenean Pseudodactylogyrus sp. The overall results of this study in terms of elvers’ performance and quality and the composition of the biofloc material and its microbial composition indicated that BFT, which is considered to be one of the most cost-effective, sustainable, and environmentally friendly farming systems due to its zero water exchange and improvement of feed conversion ratio by the dietary contribution of bioflocs, may be satisfactorily used for farming European eels elvers at a density of 2 kg/m³. However, further studies are needed to test this technology with older eel stages.