  This work is based on high quality integral-field spectroscopic data obtained
with the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope
(VLT). The 21 brightest ($m_B\leq 15$ mag) early-type galaxies (ETGs) inside
the virial radius of the Fornax cluster are observed out to distances of
$\sim2-3\ R_{\rm e}$. Deep imaging from the VLT Survey Telescope (VST) is also
available for the sample ETGs. We investigate the variation of the galaxy
structural properties as a function of the total stellar mass and cluster
environment. Moreover, we correlate the size scales of the luminous components
derived from a multi-component decomposition of the VST surface-brightness
radial profiles of the sample ETGs with the MUSE radial profiles of stellar
kinematic and population properties. The results are compared with both
theoretical predictions and previous observational studies and used to address
the assembly history of the massive ETGs of the Fornax cluster. We find that
galaxies in the core and north-south clump of the cluster, which have the
highest accreted mass fraction, show milder metallicity gradients in their
outskirts than the galaxies infalling into the cluster. We also find a
segregation in both age and metallicity between the galaxies belonging to the
core and north-south clump and the infalling galaxies. The new findings fit
well within the general framework for the assembly history of the Fornax
cluster.
