How do you calculate the correct charge on F after F2 dissociates?
If you have two fragments that are very far apart, certain quantum chemistry methods can cause spurious effects from including both fragments in the same calculation.  A well known example of this is dissociation curves for $\ce{H2}$ with Restricted Hartree Fock.

By using a density based method, we are less likely to localise the electrons on any one atoms in integer quantities.  A wavefunction method such as Hartree Fock, which places integer electrons in well defined molecular orbitals is more likely to create this localisation.  If you need higher accuracy, MP2 or coupled cluster may be of more use.

In fact I have achieved Mulliken charges of +2 and +3 on the two different atoms at 10 angstrom separation using Hartree Fock, with a cc-PVTZ basis set in Gaussian 09.

If you insist on using DFT you should use some chemical/physical intuition to partition this system.  From experiment, i.e. time of flight spectrometry, we know that the atoms have integer charge when they strike a detector, and dispersion interactions over that distance are going to very small compared to the coulomb attract of the other atom as a point charge.  So instead you can calculate the energies of the energies of the individual $\ce{F^n+}$ for $n=0,1,2,3,4,5$.  The combination of atoms with total charge $+5$ and the lowest energy, considering the classical coulomb attraction between them, is probably the product of the dissociation.

Gaussian input used:

%chk=FF_HF.chk
%nproc=1
%mem=4GB
# UHF/CC-PVTZ NoSymm

F2 5 plus Ion

5 2
 F      0.00000000    0.00000000   -5.00000000
 F      0.00000000    0.00000000    5.00000000