Binding energies of high-L Rydberg states (L^3 7) of Th2+ with n=27-29 were studied using the Resonant Excitation Stark Ionization Spectroscopy (RESIS) method. The core of the Th2+ Rydberg ion is the Fr-like ion Th3+ whose ground state is a 5 2F5/2 level. The large core angular momentum results in a complex Rydberg fine structure pattern consisting of six levels for each value of L that is only partially resolved in the RESIS excitation spectrum. The pattern is further complicated, especially for the relatively low L levels, by strong non-adiabatic effects due to the low-lying 6d levels. Analysis of the observed RESIS spectra leads to determination of five properties of the Th3+ ion: its electric quadrupole moment, Q = 0.54(4), its adiabatic scalar and tensor dipole polarizabilities, ad,0 = 15.42(17) and ad,2 = -3.6(1.3), and the dipole matrix elements connecting the ground 52F5/2 level to the low lying 62D3/2 and 62D5/2 levels, |<52F5/2||D||62D3/2>| = 1.435(10) and |<52F5/2||D||62D5/2>| = 0.414(24). All are in atomic units. These are compared with theoretical calculations.