  We present an analysis of Euclid observations of a 0.5 deg$^2$ field in the
central region of the Fornax galaxy cluster that were acquired during the
performance verification phase. With these data, we investigate the potential
of Euclid for identifying GCs at 20 Mpc, and validate the search methods using
artificial GCs and known GCs within the field from the literature. Our analysis
of artificial GCs injected into the data shows that Euclid's data in $I_{\rm
E}$ band is 80% complete at about $I_{\rm E} \sim 26.0$ mag ($M_{V\rm } \sim
-5.0$ mag), and resolves GCs as small as $r_{\rm h} = 2.5$ pc. In the $I_{\rm
E}$ band, we detect more than 95% of the known GCs from previous spectroscopic
surveys and GC candidates of the ACS Fornax Cluster Survey, of which more than
80% are resolved. We identify more than 5000 new GC candidates within the field
of view down to $I_{\rm E}$ mag, about 1.5 mag fainter than the typical GC
luminosity function turn-over magnitude, and investigate their spatial
distribution within the intracluster field. We then focus on the GC candidates
around dwarf galaxies and investigate their numbers, stacked luminosity
distribution and stacked radial distribution. While the overall GC properties
are consistent with those in the literature, an interesting over-representation
of relatively bright candidates is found within a small number of relatively
GC-rich dwarf galaxies. Our work confirms the capabilities of Euclid data in
detecting GCs and separating them from foreground and background contaminants
at a distance of 20 Mpc, particularly for low-GC count systems such as dwarf
galaxies.
