We present a one-dimensional, local thermodynamic equilibrium homogeneous analysis of 132 stars observed at high resolution with ESPaDOnS. This represents the largest sample observed at high resolution (R ~ 40 000) from the Pristine survey. This sample is based on the first version of the Pristine catalogue and covers the full range of metallicities from [Fe/H] ~-3 to ~+0.25, with nearly half of our sample (58 stars) composed of very metal-poor (VMP) stars ([Fe/H] ≤ -2). This wide range of metallicities provides the opportunity of a new detailed study of the Milky Way stellar population. Because it includes both dwarf and giant stars, it also enables the analysis of any potential bias induced by the Pristine selection process. Based on Gaia EDR3, the orbital analysis of this Pristine-ESPaDOnS sample shows that it is composed of 65 halo stars and 67 disc stars. After a general assessment of the sample chemical properties with the α-elements Mg and Ca, we focus on the abundance of carbon and the neutron capture elements Ba and Sr. While most of our VMP subsample is carbon normal, we also find that 14 stars out of the 38 stars with [Fe/H] ≤ -2 and measured carbon abundances turn out to be carbon-enhanced metal-poor (CEMP) stars. We show that these CEMP stars are nearly exclusively (i.e. 12 stars out of 14) in the regime of low luminosity, unevolved, dwarf stars, which we interpret as the consequence of bias of the Pristine filter against C-rich giants. Among the VMP stars, we identify two CEMP stars with no enhancement in neutron-capture process elements and another one enriched in s-process element. Finally, one VMP star is found with a very low [Sr/Fe] abundance ratio for its metallicity, as expected if it had been accreted from an ultra-faint dwarf galaxy.