We acquired radial velocities of a significant number of globular clusters (GCs) on wide fields between galaxies in the nearby Fornax cluster of galaxies, in order to derive their velocity dispersion radial profile and to probe the dynamics of the cluster. We used FLAMES on the VLT to obtain accurate velocities for 149 GCs, within a ~500x150 kpc strip centered on NGC 1399, the Fornax central galaxy. These objects are at the very bright tail (M_V < -9.5) of the GC luminosity function, overlapping the so-called ``ultra-compact dwarfs'' magnitude range. Eight of the brightest FLAMES-confirmed members indeed show hints of resolution in the subarcsecond pre-imaging data we used for selecting the ~500 targets for FLAMES spectroscopy. Ignoring the GCs around galaxies by applying 3d_25 diameter masks, we find 61 GCs of 20.0 < V < 22.2 lying in the intra-cluster (IC) medium. The velocity dispersion of the population of ICGCs is 200 km/s at ~150 kpc from the central NGC 1399 and rises to nearly 400 km/s at 200 kpc, a value which compares with the velocity dispersion of the population of dwarf galaxies, thought to be infalling from the surroundings of the cluster.