We present a wide-field study of the globular cluster (GC)/low-mass X-ray binary (LMXB) connection in the giant elliptical NGC 1399. The large field of view of the Advanced Camera for Surveys/WFC, combined with Hubble Space Telescope and Chandra high resolution, allow us to constrain the LMXB formation scenarios in elliptical galaxies. We confirm that NGC 1399 has the highest LMXB fraction in GCs of all nearby elliptical galaxies studied so far, even though the exact value depends on galactocentric distance due to the interplay of a differential GC versus galaxy light distribution and the GC color dependence. In fact, LMXBs are preferentially hosted by bright, red GCs out to > 5R(eff) of the galaxy light. The finding that GCs hosting LMXBs follow the radial distribution of their parent GC population argues against the hypothesis that the external dynamical influence of the galaxy affects the LMXB formation in GCs. On the other hand, field-LMXBs closely match the host galaxy light, thus indicating that they are originally formed in situ and not inside GCs. We measure GC structural parameters, finding that the LMXB formation likelihood is influenced independently by mass, metallicity, and GC structural parameters. In particular, the GC central density plays a major role in predicting which GCs host accreting binaries. Finally, our analysis shows that LMXBs in GCs are marginally brighter than those in the field, and in particular the only color-confirmed GC with L-X > 10(39) erg s(-1) shows no variability, which may indicate a superposition of multiple LMXBs in these systems.