This paper is based on the multi-band (ugri) Fornax Deep Survey (FDS) with the VLT Survey Telescope (VST). We study bright early-type galaxies (m_B_<15mag) in the 9 square degrees around the core of the Fornax cluster, which covers the virial radius (R_vir~0.7Mpc). The main goal of the present work is to provide an analysis of the light distribution for all galaxies out to unprecedented limits (in radius and surface brightness) and to release the main products resulting from this analysis in all FDS bands. We give an initial comprehensive view of the galaxy structure and evolution as a function of the cluster environment. From the isophote fit, we derived the azimuthally averaged surface brightness profiles, the position angle, and ellipticity profiles as a function of the semi-major axis. In each band, we derived the total magnitudes, effective radii, integrated colours, and stellar mass-to-light ratios. The long integration times, the arcsec-level angular resolution of OmegaCam@VST, and the large covered area of FDS allow us to map the light and colour distributions out to large galactocentric distances (up to about 10^-15^Re) and surface brightness levels beyond mu_r_=27mag/arcsec^2^ (mu_B_>28mag/arcsec^2^). Therefore, the new FDS data allow us to explore in great detail the morphology and structure of cluster galaxies out to the region of the stellar halo. The analysis presented in this paper allows us to study how the structure of galaxies and the stellar population content vary with the distance from the cluster centre. In addition to the intra-cluster features detected in previous FDS works, we found a new faint filament between FCC 143 and FCC 147, suggesting an ongoing interaction. The observations suggest that the Fornax cluster is not completely relaxed inside the virial radius. The bulk of the gravitational interactions between galaxies happens in the W-NW core region of the cluster, where most of the bright early-type galaxies are located and where the intra-cluster baryons (diffuse light and globular clusters) are found. We suggest that the W-NW sub-clump of galaxies results from an infalling group onto the cluster, which has modified the structure of the galaxy outskirts (making asymmetric stellar halos) and has produced the intra-cluster baryons (ICL and GCs), concentrated in this region of the cluster.