The structural, vibrational, and electronic properties of low-temperature supercooled GeTe4 are studied using density functional theory (DFT). Two models have been considered: an ordinary melt-quenched system containing a majority of defect-octahedral germanium atoms, and a relaxed one obtained from a quenched SiTe4 rescaled structure which contains mostly tetrahedral germanium, while leaving the Te environment preserved. The tetrahedral system exhibits an increased agreement with the experimental structure factor S(k), the pair distribution function g(r), and the infrared absorption spectrum. It is suggested that the fraction of tetrahedral Ge must be higher as usually believed. In addition, we provide the calculation of the 125Te wideline NMR spectra. While the latter do not agree with recent experimental findings, both systems exhibit important significant differences in the widths of the computed spectra. These exploratory calculations clearly show that NMR will be an interesting probe that deserves further investigations for the experimental determination of the local geometry.