Metal-poor stars formed from a gas enriched by the ejecta of the explosion of one/few generations of first massive stars. With the Pristine photometry combined with the Gaia data, we selected a sample of bright giants metal-poor candidates to be observed at high resolution. Of the 43 stars observed, 36 were confirmed to be metal-poor, supporting the high success-rate of Pristine in selecting metal-poor stars. We centred the investigation on Cu and Zn, which are elements usually neglected, also because they are the 'killing elements' for identifying the Pair Instability Supernovae (PISN) descendants, the explosion of very massive first stars. We derived detailed chemical abundances of 22 species of 18 elements for 36 giant stars. The study of the kinematics of the stars in the sample revealed the presence of metal-poor stars on disc-like orbits (17 per cent of the sample) and even on thin disc orbits (8 per cent of the sample). Four stars are members of the Gaia-Sausage-Enceladus, one star is also likely a member of it. Three stars in the sample (TYC 1118-595-1, TYC 2207-992-1, and TYC 1194-507-1) show a chemical pattern compatible with the one theoretically derived for the PISN descendants, i.e. stars formed out from a gaseous environment enriched by PISN (>50 per cent level) and subsequent generations of normal stars evolving as core-collapse SNe.