The current paper reports a global investigation of all excited states below the ionic limit Fr+Na- of FrNa molecule following diabatic and adiabatic representations. The adiabatic and diabatic potential energy curves (PECs) for Sigma(+), Pi, and Delta symmetries have been calculated for a dense grid of internuclear distances. The transition and permanent dipole moments (TDM and PDM) have been reported for both representations. Regarding the pseudopotential approach and full valence configuration interaction (FCI), the ab initio computation has been performed. Furthermore, the diabatization method was achieved by the use of the variational effective Hamiltonian theory (VEH). This latter served to assess the nonadiabatic coupling between the treated adiabatic states and to eliminate it employing a suitable unitary transformation matrix. The detailed computation of the PECs and PDM and TDM curves of the ground and excited states play a key role to coordinate experimental efforts in order to create cold and ultracold molecules in their ground stable rovibrational levels.