We present Atacama Large Millimeter/submillimeter Array [C II] 158 μm line and underlying far-infrared (FIR) continuum emission observations (0 70 × 0 56 resolution) toward HSC J124353.93+010038.5 (J1243+0100) at z = 7.07, the only low-luminosity (M 1450 > −25 mag) quasar currently known at z > 7. The FIR continuum is bright (1.52 mJy) and resolved with a total luminosity of L FIR = 3.5 × 10 12 L e . The spatially extended component is responsible for ∼40% of the emission. The area-integrated [C II] spectrum shows a broad wing (FWHM = 997 km s −1 , L [C II] = 1.2 × 10 9 L e ), as well as a bright core (FWHM = 235 km s −1 , L [C II] = 1.9 × 10 9 L e ). This wing is the first detection of a galactic-scale quasar-driven outflow (atomic outflow rate >447 M e yr −1 ) at z > 7. The estimated large mass-loading factor of the total outflow (e.g., 9 relative to the [C II]-based star formation rate) suggests that this outflow will soon quench the star formation of the host. The core gas dynamics are governed by rotation, with a rotation curve suggestive of a compact bulge (∼3.3 × 10 10 M e ), although it is not yet spatially resolved. Finally, we found that J1243+0100 has a black hole mass-to-dynamical mass (and -to-bulge mass) ratio of ∼0.4% (∼1%), consistent with the local value within the uncertainties. Our results therefore suggest that the black hole-host coevolution relation is already in place at z ∼ 7 for this object.Unified Astronomy Thesaurus concepts: Quasars (1319); AGN host galaxies (2017); Active galaxies (17); Interstellar medium (847); Submillimeter astronomy (1647); High-redshift galaxies (734); Galaxy evolution (594)