A possible pathway for understanding the events and the mechanisms involved in galaxy formation and evolution is an in-depth comprehension of the galactic and inter-galactic fossil sub-structures with long dynamical times-scales: stars in the field and in stellar clusters. This paper continues the series of the Fornax Deep Survey (FDS). Following the previous studies dedicated to extended Fornax cluster members, in this paper we present the catalogs of compact stellar systems in the Fornax cluster as well as extended background sources and point-like sources. We derive ugri photometry of ~1.7 million sources over the ~21 square degree area of FDS centered on the bright central galaxy NGC1399. For a wider area, of ~27 square degrees extending in the direction of NGC1316, we provide gri photometry for ~3.1 million sources. To improve the morphological characterization of sources we generate multi-band image stacks by coadding the best seeing gri-band single exposures with a cut at FWHM<=0.9". We use the multi-band stacks as master detection frames, with a FWHM improved by ~15% and a FWHM variability from field to field reduced by a factor of ~2.5 compared to the pass-band with best FWHM, namely the r-band. The identification of compact sources, in particular of globular clusters (GC), is obtained from a combination of photometric (e.g. colors, magnitudes) and morphometric (e.g. concentration index, elongation, effective radius) selection criteria, by also taking as reference the properties of sources with well-defined classification from spectroscopic or high-resolution imaging data. Using the FDS catalogs, we present a preliminary analysis of globular cluster (GC) distributions in the Fornax area. The study confirms and extends further previous results which were limited to a smaller survey area. We observe the inter-galactic population of GCs, a population of mainly blue GCs centered on NGC1399, extends over ~0.9Mpc, with an ellipticity ~0.65 and a small tilt in the direction of NGC1336. Several sub-structures extend over ~0.5Mpc along various directions. Two of these structures do not cross any bright galaxy; one of them appears to be connected to NGC1404, a bright galaxy close to the cluster core and particularly poor of GCs. Using the gri catalogs we analyze the GC distribution over the extended FDS area, and do not find any obvious GC sub-structure bridging the two brightest cluster galaxies, NGC1316 and NGC1399. Although NGC1316 is more than twice brighter of NGC1399 in optical bands, using gri data, we estimate a factor of ~3-4 richer GC population around NGC1399 compared to NGC1316, out to galactocentric distances of ~40' or ~230kpc