  In this paper, we report results of simulations, in the framework of both
EuPRAXIA \cite{Walk2017} and EuPRAXIA@SPARC\_LAB \cite{Ferr2017} projects,
aimed at delivering a high brightness electron bunch for driving a Free
Electron Laser (FEL) by employing a plasma post acceleration scheme. The
boosting plasma wave is driven by a tens of \SI{}{\tera\watt} class laser and
doubles the energy of an externally injected beam up to \GeV{1}. The injected
bunch is simulated starting from a photoinjector, matched to plasma, boosted
and finally matched to an undulator, where its ability to produce FEL radiation
is verified to yield $O(\num{e11})$ photons per shot at \nm{2.7}.
