  (Abridged) We have surveyed four globular clusters in the Fornax dwarf galaxy
for RR Lyrae stars, using archival HST observations. We identify 197 new RR
Lyrae stars in these four clusters. Despite the short observational baseline,
we derive periods, light-curves, and photometric parameters for each. The
Fornax clusters have exceptionally large RR Lyrae specific frequencies compared
with the Galactic globular clusters. Furthermore, the Fornax cluster RR Lyrae
stars are unusual in that their characteristics are intermediate between the
two Galactic Oosterhoff groups. In this respect the Fornax clusters are similar
to the field populations in several dwarf galaxies. We revise previous
measurements of the HB morphology in each cluster. The Fornax clusters closely
resemble the ``young'' Galactic halo population defined by Zinn. The existence
of the second parameter effect among the Fornax clusters is also confirmed.
Finally, we determine foreground reddening and distance estimates for each
cluster. We find a mean distance modulus to Fornax of (m-M)_0 = 20.66 +/- 0.03
(random) +/- 0.15 (systematic). Our measurements are consistent with a line of
sight depth of 8-10 kpc for this galaxy, matching its projected dimensions, and
incompatible with tidal model explanations for the observed high velocity
dispersions in many dSph galaxies. Dark matter dominance is suggested.
