  Measuring the abundances of C- and O-bearing species in exoplanet atmospheres
enables us to constrain the C/O ratio, that contains indications about the
planet formation history. With a wavelength coverage going from 0.95 to 2.5
microns, the high-resolution (R$\sim$70 000) spectropolarimeter SPIRou can
detect spectral lines of major bearers of C and O in exoplanets. Here we
present our study of SPIRou transmission spectra of WASP-76 b acquired for the
ATMOSPHERIX program. We applied the publicly available data analysis pipeline
developed within the ATMOSPHERIX consortium, analysing the data using 1-D
models created with the petitRADTRANS code, with and without a grey cloud deck.
We report the detection of H$_2$O and CO at a Doppler shift of around -6
km.s$^{-1}$, consistent with previous observations of the planet. Finding a
deep cloud deck to be favoured, we measured in mass mixing ratio (MMR)
log(H$_2$O)$_{MMR}$ = -4.52 $\pm$ 0.77 and log(CO)$_{MMR}$ = -3.09 $\pm$ 1.05
consistent with a sub-solar metallicity to more than 1$\sigma$. We report
3$\sigma$ upper limits for the abundances of C$_2$H$_2$, HCN and OH. We
estimated a C/O ratio of 0.94 $\pm$ 0.39 ($\sim$ 1.7 $\pm$ 0.7 x solar, with
errors indicated corresponding to the 2$\sigma$ values) for the limbs of
WASP-76 b at the pressures probed by SPIRou. We used 1-D ATMO forward models to
verify the validity of our estimation. Comparing them to our abundance
estimations of H$_2$O and CO, as well as our upper limits for C$_2$H$_2$, HCN
and OH, we found that our results were consistent with a C/O ratio between 1
and 2 x solar, and hence with our C/O estimation. Finally, we found indications
of asymmetry for both H$_2$O and CO when investigating the dynamics of their
signatures, pointing to a complex scenario involving possibly both a
temperature difference between limbs and clouds being behind the asymmetry this
planet is best known for.
