  In this work we investigate the possibility to create cold Fr$\_2$, RbFr, and
CsFr molecules through photoassociation of cold atoms. Potential curves,
permanent and transition dipole moments for the Francium dimer and for the RbFr
and RbCs molecules are determined for the first time. The Francium atom is
modelled as a one valence electron moving in the field of the Fr$^+$ core,
which is described by a new pseudopotential with averaged relativistic effects,
and including effective core polarization potential. The molecular calculations
are performed for both the ionic species Fr$\_2^+$, RbFr$^+$, CsFr$^+$ and the
corresponding neutral, through the CIPSI quantum chemistry package where we
used new extended gaussian basis sets for Rb, Cs, and Fr atoms. As no
experimental data is available, we discuss our results by comparison with the
Rb$\_2$, Cs$\_2$, and RbCs systems. The dipole moment of CsFr reveals an
electron transfer yielding a Cs$^+$Fr$^-$ arrangement, while in all other mixed
alkali pairs the electron is transferred towards the lighter species. Finally
the perturbative treatment of the spin-orbit coupling at large distances
predicts that in contrast with Rb$\_2$ and Cs$\_2$, no double-well excited
potential should be present in Fr$\_2$, probably preventing an efficient
formation of cold dimers via photoassociation of cold Francium atoms.
