Molecular structures in the electronically excited (S-1) and cationic (D-0) states of 2-fluorothioanisole (2-FTA) have been precisely refined from the real-time dynamics of the femtosecond (fs) wavepacket prepared by the coherent excitation of the Franck-Condon active out-of-plane torsional modes in the S-1 <- S-0 transition at 285 nm. The simulation to reproduce the experiment in terms of the beating frequencies gives the nonplanar geometry of 2-FTA in S-1, where the out-of-plane dihedral angle (phi) of the S-CH3 moiety is 51 degrees with respect to the molecular plane. The behavior of the fs wavepacket in terms of the amplitudes and phases with the change of the probe (ionization) wavelength (lambda(probe) = 300-330 nm) provides the otherwise veiled structure of the cationic D-0 state. While the 2-FTA cation adopts the planar geometry (phi = 0 degrees) at the global minimum, it is found to have a vertical minimum at phi approximate to 135 degrees from the perspective of the D-0 <- S-1 vertical transition. Ab initio calculations support the experiment quite well although the simulation using the model potentials could improve the match with the experiment, giving the new interpretation for the previously disputed photoelectron spectroscopic results.