We combine ALMA and MUSE-NFM (narrow field mode, with full four-laser adaptive optics correction) data at 0.15 arcsec spatial resolution of the archetypical AGN-starburst "composite" galaxy NGC 7130. We present the discovery of a small 0″.2 (60 pc) radius kinematically decoupled core or small bi-polar outflow, as well as a larger-scale outflow. We confirm the existence of star-forming knots arranged in an 0″.58 (185 pc) radius ring around the Seyfert 1.9 nucleus, previously observed from UV and optical Hubble Space Telescope and CO(6-5) ALMA imaging. An extinction map derived from the MUSE data highlights the regions of enhanced CO emission as clearly seen in the ALMA data. 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″ (640 pc) radius which we interpret as an outflow originating in the AGN. The plume is not visible morphologically, but is clearly characterised in our data by emission lines 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 disk. An 0″.2-radius circumnuclear area of positive and negative velocities indicates a tiny inner disk or a small bipolar outflow, only observable when combining the integral field spectroscopic capabilities of MUSE with full adaptive optics.