  Narrow-band imaging surveys allow the study of the spectral characteristics
of galaxies without the need of performing their spectroscopic follow-up. In
this work, we forward-model the Physics of the Accelerating Universe Survey
(PAUS) narrow-band data. The aim is to improve the constraints on the spectral
coefficients used to create the galaxy spectral energy distributions (SED) of
the galaxy population model in Tortorelli et al. 2020. In that work, the model
parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey
(CFHTLS) data using Approximate Bayesian Computation (ABC). This led to
stringent constraints on the B-band galaxy luminosity function parameters, but
left the spectral coefficients only broadly constrained. To address that, we
perform an ABC inference using CFHTLS and PAUS data. This is the first time our
approach combining forward-modelling and ABC is applied simultaneously to
multiple datasets. We test the results of the ABC inference by comparing the
narrow-band magnitudes of the observed and simulated galaxies using Principal
Component Analysis, finding a very good agreement. Furthermore, we prove the
scientific potential of the constrained galaxy population model to provide
realistic stellar population properties by measuring them with the SED fitting
code \textsc{CIGALE}. We use CFHTLS broad-band and PAUS narrow-band photometry
for a flux-limited ($\mathrm{i}<22.5$) sample of galaxies up to redshift
$\mathrm{z \sim 0.8}$. We find that properties like stellar masses,
star-formation rates, mass-weighted stellar ages and metallicities are in
agreement within errors between observations and simulations. Overall, this
work shows the ability of our galaxy population model to correctly
forward-model a complex dataset such as PAUS and the ability to reproduce the
diversity of galaxy properties at the redshift range spanned by CFHTLS and
PAUS.
