We present ALMA observations of CO isotopologues and high-density molecular tracers (HCN, HCO+, CN, etc.) in NGC 7465, an unusually gas-rich early-type galaxy that acquired its cold gas recently. In the inner 300 pc, the molecular gas kinematics are misaligned with respect to all other galaxy components; as the gas works its way inward, it is torqued into polar orbits about the stellar kinematically decoupled core (KDC), indicating that the stellar KDC is not related to the current gas accretion event. The galaxy also exhibits unusually high (CO)-C-12/(CO)-C-13 line ratios in its nucleus but typical (CO)-C-13/(CO)-O-18 ratios. Our calculations show that this result does not necessarily indicate an unusual [(CO)-C-12/(CO)-C-13] abundance ratio but rather that (CO)-C-12 (1-0) is optically thin due to high temperatures and/or large line widths associated with the inner decoupled, misaligned molecular structure. Line ratios of the higher-density tracers suggest that the densest phase of molecular gas in NGC 7465 has a lower density than is typical for nearby galaxies, possibly as a result of the recent gas accretion. All of the observed molecular properties of NGC 7465 are consistent with it having acquired its molecular (and atomic) gas from a spiral galaxy. Further detailed studies of the CO isotopologues in other early-type galaxies would be valuable for investigating the histories of those that may have acquired their gas from dwarfs. Finally, these ALMA data also show an unidentified line source that is probably a background galaxy similar to those found at z = 1-3 in blind CO surveys.