They could have used a modified version of FFXI's hate system, in which spells, attacks, basically everything generates different amounts of hate on a character which will focus the mob's attention. In FFXI, white mages in particular get hate frequently because of their constant curing. I tried to pay attention to this possibility as I played, but I couldn't ever tell for certain if this was the case or if a gambit was producing the results.
Most likely though, the mobs' gambits are targeting fran for some reason. Remember, they have more/different gambits than our PC's do, so it might be something that's not so obvious. It's hard to speculate, but the only method I can think of to determine exactly what's going on is to mess with Fran's stats. First compare her stats to everyone else's and if she has something that's obviously higher than the others then that may be what's giving her so much hate. eg. Foe: Highest Str --> Attack. Move her hp/mp/str/def/etc up and down and see if you get any results.