  We present the discovery of a small kinematically decoupled core of
0.2$^{\prime\prime}$ (60 pc) in radius as well as an outflow jet in the
archetypical AGN-starburst "composite" galaxy NGC 7130 from integral field data
obtained with the adaptive optics-assisted MUSE-NFM instrument on the VLT.
Correcting the already good natural seeing at the time of our science
verification observations with the four-laser GALACSI AO system, we reach an
unprecedented spatial resolution at optical wavelengths of around
0.15$^{\prime\prime}$. We confirm the existence of star-forming knots arranged
in a ring of 0.58$^{\prime\prime}$ (185 pc) in radius around the nucleus,
previously observed from UV and optical Hubble Space Telescope and CO(6-5) ALMA
imaging. We determine the position of the nucleus as the location of a peak in
gas velocity dispersion. A plume of material extends towards the NE from the
nucleus until at least the edge of our field of view at 2$^{\prime\prime}$ (640
pc) radius which we interpret as an outflow jet originating in the AGN. The
plume is not visible morphologically, but is clearly characterised in our data
by emission-line ratios characteristic of AGN emission, enhanced gas velocity
dispersion, and distinct non-circular gas velocities. Its orientation is
roughly perpendicular to the line of nodes of the rotating host galaxy disc. A
circumnuclear area of positive and negative velocities of 0.2$^{\prime\prime}$
in radius indicates a tiny inner disc, which can only be seen after combining
the integral field spectroscopic capabilities of MUSE with adaptive optics.
