In order to elucidate the ionization dynamics, in particular the vibrational distribution, of H2S+(A) produced by the Penning ionization of H2S with He-*(2 S-3) atoms, the Franck-Condon factors (FCFs) were presented for the H2S(X)-->H2S+(X,A) ionization and the H2S+(A-X) transition, and Einstein's A coefficients were presented for the latter transition. The FCFs were obtained by quantum vibrational calculations using the global potential energy surfaces (PESs) of H2S(X (1)A(1)) and H2S+(X B-2(1),A (2)A(1),B B-2(2)) electronic states. The global PESs were determined by the multireference configuration interaction calculations with the Davidson correction and the interpolant moving least squares method combined with the Shepard interpolation. The obtained FCFs exhibit that the H2S+(X) state primarily populates the vibrational ground state since its equilibrium geometry is almost equal to that of H2S(X), while the bending mode (nu(2)) is strongly enhanced for the H2S+(A) state; the maximum in the population is around nu(2)=6-7. In the same manner, the bending progressions are expected to consist of the great part of the H2S+(A-X) emission. A detailed comparison with the experimental study for this system is reported in the accompanying paper, Paper II. (C) 2003 American Institute of Physics.