Photodetachment spectroscopy of the FH2– and FD2– anions allows for the direct observation of reactive resonances in the benchmark reaction F + H2 → HF + H. Using cooled anion precursors and a high-resolution electron spectrometer, we observe several narrow peaks not seen in previous experiments. Theoretical calculations, based on a highly accurate F + H2 potential energy surface, convincingly assign these peaks to resonances associated with quasibound states in the HF + H and DF + D product arrangements and with a quasibound state in the transition state region of the F + H2 reaction. The calculations also reveal quasibound states in the reactant arrangement, which have yet to be resolved experimentally.