POLAR-2 is a dedicated gamma-ray polarimeter currently foreseen to be launched towards the China Space Station around 2027. The design of the detector is based on the legacy of its predecessor mission POLAR which was launched in 2016. POLAR-2 aims to measure the polarization of the Gamma-ray Burst prompt emission within the 30–800 keV energy range. Thanks to its high sensitivity to gamma-ray polarization, as well as its large effective area, POLAR-2 will provide the most precise measurements of this type to date. Such measurements are key to improve our understanding of the astrophysical processes responsible for Gamma-Ray Bursts. The detector consists of a segmented array of plastic scintillator bars, each one of which is read out by a Silicon PhotoMultiplier channel. The flight model of POLAR-2 will contain a total of 6400 scintillators. These are divided into 100 groups of 64 bars each, in so-called polarimeter modules. In recent years, the collaboration has designed and produced the first prototypes of these polarimeter modules and subjected these to space qualification tests. In addition, in April 2023, the first of these modules were calibrated using fully polarized gamma-ray beams at the European Synchrotron Radiation Facility (ESRF) in France. In this work, we will present the results of this calibration campaign and compare these to the simulated performance of the POLAR-2 modules. Potential improvements to the design are also discussed. Finally, the measurements are used, in combination with the verified simulation framework, to estimate the scientific performance of the full POLAR-2 detector and compare it to its predecessor.