As part of the Fornax Deep Survey with the ESO VLT Survey Telescope, we present new g- and r-band mosaics of the SW group of the Fornax Cluster. It covers an area of 3 x 2 square degrees around the central galaxy NGC 1316. The deep photometry, the high spatial resolution of OmegaCam, and the large covered area allow us to study the galaxy structure, trace stellar halo formation, and look at the galaxy environment. We map the surface brightness profile out to 33' (similar to 200 kpc similar to 15R(e)) from the galaxy center, down to mu(g) similar to 31 mag arcsec(-2) and mu(T) similar to 29 mag arcsec(-2). This allow us to estimate the scales of the main components dominating the light distribution, which are the central spheroid, inside 5'.5 (similar to 33 kpc), and the outer stellar envelope. Data analysis suggests that we are catching in the act the second phase of the mass assembly in this galaxy, since the accretion of smaller satellites is going on in both components. The outer envelope of NGC 1316 still hosts the remnants of the accreted satellite galaxies that are forming the stellar halo. We discuss the possible formation scenarios for NGC 1316, by comparing the observed properties (morphology, colors, gas content, kinematics, and dynamics) with predictions from cosmological simulations of galaxy formation. We find that (i) the central spheroid could result from at least one merging event (it could be a preexisting early-type disk galaxy with a lower-mass companion) and (ii) the stellar envelope comes from the gradual accretion of small satellites.