  The metallicity spread, or the metallicity trend along the evolutionary
sequence of a globular cluster, is a rich source of information to help
understand the cluster physics (e.g. multiple populations) and stellar physics
(e.g. atomic diffusion). Low-resolution integral-field-unit spectroscopy in the
optical with the MUSE is an attractive prospect if it can provide these
diagnostics because it allows us to extract spectra of a large fraction of the
cluster stars. We investigate the possibilities of full-spectrum fitting to
derive stellar parameters and chemical abundances at low spectral resolution
(R~2000). We reanalysed 1584 MUSE spectra of 1061 stars above the turn-off of
NGC 6397 using FERRE and employing two different synthetic libraries. We derive
the equivalent iron abundance \fehe for fixed values of \afe. We find that (i)
the interpolation schema and grid mesh are not critical for the precision,
metallicity spread, and trend; (ii) with the two grids, \fehe increases by ~0.2
dex along the sub-giant branch, starting from the turn-off of the main
sequence; (iii) restricting the wavelength range to the optical decreases the
precision significantly; and (iv) the precision obtained with the synthetic
libraries is lower than the precision obtained previously with empirical
libraries. Full-spectrum fitting provides reproducible results that are robust
to the choice of the reference grid of synthetic spectra and to the details of
the analysis. The \fehe increase along the sub-giant branch is in stark
contrast with the nearly constant iron abundance previously found with
empirical libraries. The precision of the measurements (0.05 dex on \fehe) is
currently not sufficient to assess the intrinsic chemical abundance spreads,
but this may change with deeper observations. Improvements of the synthetic
spectra are still needed to deliver the full possibilities of full-spectrum
fitting.
