We aim to constrain the chemo-dynamical properties of the Sagittarius (Sgr) dwarf galaxy using carbon abundances. At low metallicities in particular, these properties reveal the early chemical evolution of a system, tracing the contributing supernovae (SNe) and how much of their ejecta eventually made it into the next stellar generation. Our sample from the Pristine Inner Galaxy Survey (PIGS) includes ∼350 metal-poor ([Fe/H] < -1.5) stars in the main body of Sgr with good quality spectroscopic observations. Our metal-poor Sgr population has a larger velocity dispersion than metal-rich Sgr from the literature, which could be explained by outside-in star formation, extreme Galactic tidal perturbations, and/or the presence of a metal-rich disc and bar + metal-poor halo. The average carbon abundance [C/Fe] in Sgr is similar to that of other classical dwarf galaxies (DGs) and consistently lower than in the Milky Way by ∼0.2-0.3 dex at low metallicities. The interstellar medium in DGs, including Sgr, may have retained yields from more energetic Population III and II supernovae (SNe), thereby reducing the average [C/Fe]. Additionally, SNe Ia producing more Fe than C would start to contribute at lower metallicity in DGs/Sgr than in the Galaxy. The presence of a [C/Fe] gradient for Sgr stars with [Fe/H] ≳ -2.0 (∼6.8 × 10 -4 dex arcmin -1 ) suggests that SNe Ia contributed to the system at those metallicities, especially in its inner regions. There is a low frequency of carbon-enhanced metal-poor (CEMP) stars in our Sgr sample. At higher metallicities and carbon abundances (i.e. mostly CEMPs), this may be due to photometric selection effects, but those are less likely to affect non-CEMP stars. Given the lower average [C/Fe] in DGs, we propose using the same CEMP definition ([C/Fe] > +0.7) as that applied to the Galaxy at large ends up underpredicting the number of CEMP stars in DGs. Burthermore, for Sgr, a cut at [C/Fe] ∼ +0.35 may be more appropriate, which brings the frequency of CEMP stars in agreement with that of the whole Galaxy.