In the context of global biodiversity loss, wildlife population monitoring is a major challenge. Some innovative techniques such as the use of drones—also called unmanned aerial vehicle/system (UAV/UAS)—offer promising opportunities. The potential of UAS-based wildlife census using high-resolution imagery is now well established for terrestrial mammals or birds that can be seen on images. Nevertheless, the ability of UASs to detect non-conspicuous species, such as small birds below the forest canopy, remains an open question. This issue can be solved with bioacoustics for acoustically active species such as bats and birds. In this context, UASs represent an interesting solution that could be deployed on a larger scale, at lower risk for the operator, and over hard-to-reach locations, such as forest canopies or complex topographies, when compared with traditional protocols (fixed location recorders placed or handled by human operators). In this context, this study proposes a methodological framework to assess the potential of UASs in bioacoustic surveys for birds and bats, using low-cost audible and ultrasound recorders mounted on a low-cost quadcopter UAS (DJI Phantom 3 Pro). The proposed methodological workflow can be straightforwardly replicated in other contexts to test the impact of other UAS bioacoustic recording platforms in relation to the targeted species and the specific UAS design. This protocol allows one to evaluate the sensitivity of UAS approaches through the estimate of the effective detection radius for the different species investigated at several flight heights. The results of this study suggest a strong potential for the bioacoustic monitoring of birds but are more contrasted for bat recordings, mainly due to quadcopter noise (i.e., electronic speed controller (ESC) noise) but also, in a certain manner, to the experimental design (use of a directional speaker with limited call intensity). Technical developments, such as the use of a winch to safely extent the distance between the UAS and the recorder during UAS sound recordings or the development of an innovative platform, such as a plane–blimp hybrid UAS, should make it possible to solve these issues.