  The optical line and continuum emission in the very high ionization Galactic
planetary nebula (PN) NGC 4361 (PN G294.1 +43.6), has been mapped with VLT MUSE
Wide Field normal mode (4750-9300A) commissioning observations. The PN is
larger than a single MUSE field and only the central 1 arcmin square was
observed in good conditions. Images in recombination and collisionally excited
emission lines were extracted and line ratios provide dust extinction, electron
density and temperature and ionic abundances. The nebula is confirmed as
optically thin in the H-ionizing continuum based on its very low He I emission,
even to the edges of the field, but is not completely optically thin. The
electron temperature Te is shown to have large-scale spatially coherent
structure, as indicated from previous spectra. Prior to this study, no low
ionization emission had been positively detected; MUSE revealed both weak
extended [N II] and [O II] and $>$100 spatially unresolved low ionization knots
(dubbed 'Freckles'). There are several linear associations of the Freckles but
none point back convincingly to the central star. The Freckle spectra show
low-moderate ionization with Te $\sim$11000 K, Ne $\sim$1500 cm$^{-3}$ and
higher extinction than the highly ionized medium, but do not clearly differ in
(He, N, O, S) abundance with respect to the extended gas. The spatial
distribution and radial velocities suggest that the Freckles belong to a thick
disk oriented perpendicular to the large-scale nebula, perhaps remnants of an
earlier structure. Within the MUSE field, a low redshift emission line galaxy
was serendipitously found hiding behind NGC 4361. The spectrum of this dwarf
galaxy was extracted from the bright foreground nebular emission: it is a low
luminosity disk galaxy at $\sim$87 Mpc with bright H II regions (12+log(O/H)
$\sim$ 8.4), probably a Magellanic irregular or low-mass spiral. (Abridged)
