  We present ALMA Band 6 observations (1.3 mm/233 GHz) of Fomalhaut and its
debris disc. The observations achieve a sensitivity of 17 $\mu$Jy and a
resolution of 0.28 arcsec (2.1 au at a distance of 7.66 pc), which are the
highest resolution observations to date of the millimetre grains in Fomalhaut's
main debris ring. The ring is tightly constrained to $139^{+2}_{-3}$ au with a
FWHM of $13\pm3$ au, following a Gaussian profile. The millimetre spectral
index is constrained to $\alpha_{mm} = -2.62\pm0.12$. We explore fitting debris
disc models in the image plane, as well as fitting models using visibility data
directly. The results are compared and the potential advantages/disadvantages
of each approach are discussed.
  The detected central emission is indistinguishable from a point source, with
a most probable flux of $0.90\pm 0.12$ mJy (including calibration
uncertainties). This implies that any inner debris structure, as was inferred
from far-Infrared observations, must contribute little to the total central
emission. Moreover, the stellar flux is less than 70\% of that predicted by
extrapolating a black body from the constrained stellar photosphere
temperature. This result emphasizes that unresolved inner debris components
cannot be fully characterized until the behaviour of the host star's intrinsic
stellar emission at millimetre wavelengths is properly understood.
