We present Atacama Large Millimeter/submillimeter Array (ALMA) [C II] 158 μm and dust continuum observations of the z = 6.79 quasar J0109-3047 at a resolution of 0.045 arcsec (~300 pc). The dust and [C II] emission are enclosed within a ~500 pc radius, with the central beam (r < 144 pc) accounting for ~25% (8%) of the total continuum ([C II]) emission. The far-infrared (FIR) luminosity density increases radially from ~5 × 10^11 Lsun kpc^-2 to a central value of ~70 × 10^11 Lsun kpc^-2 (SFRD ~50-700 Msun/yr kpc^-2). The [C II] kinematics are dispersion dominated with a constant velocity dispersion of 137+-6 km s^1. The constant dispersion implies that the underlying mass distribution is not centrally peaked, consistent with the expectations of a flat gas mass profile. The lack of an upturn in velocity dispersion within the central beam is inconsistent with a black hole mass greater than M BH < 6.5 × 10^8 Msun (2sigma level), unless highly fine-tuned changes in the interstellar medium properties conspire to produce a decrease of the gas mass in the central beam comparable to the black hole mass. Our observations therefore imply either that (a) the black hole is less massive than previously measured, or (b) the central peak of the FIR and [C II] emission are not tracing the location of the black hole, as suggested by the tentative offset between the near-infrared position of the quasar and the ALMA continuum emission.