  The early-type galaxy NGC 1316 hosts about 10^7 solar masses of dust within a
central radius of 5 kpc. These prominent dust structures are believed to have
an external origin, which is also a popular interpretation for other dusty
early-type galaxies. We use archival Hubble Space Telescope/ACS data to
construct colour maps that delineate the dust pattern in detail, and we compare
these data with maps constructed with data from MUSE of the VLT at the European
Southern Observatory. Twelve MUSE pointings in wide field mode form a mosaic of
the central 3.3'x2.4'. We use the tool PyParadise to fit the stellar
population. We use the residual emission lines and the residual interstellar
absorption NaI D-lines, and we measure line strengths, the velocity field, and
the velocity dispersion field. The emission lines resemble LINER lines, with
[NII] being the strongest line everywhere. Ionising sources are plausibly the
post-asymptotic giant branch stars of the old or intermediate-age stellar
population. There is a striking match between the dust structures, ionised gas,
and atomic gas distributions, the last of which is manifested by interstellar
absorption residuals of the stellar NaI D-lines. In the dust-free regions, the
interstellar NaI D-lines appear in emission, which is indicative of a galactic
wind. The velocity field of the ionised gas (and thus of the dust) is
characterised by small-scale turbulent movements that indicate short lifetimes.
At the very centre, a bipolar velocity field of the ionised gas is observed,
which we interpret as an outflow. We identify a strongly inclined gaseous dusty
disc along the major axis of NGC1316. A straight beam of ionised gas with a
length of about 4 kpc emanates from the centre. Our findings are strongly
suggestive of a dusty outflow. Nuclear outflows may be important dust-producing
machines in galaxies. (Abridged)
