What still baffles me is that however unique you want your idea to be, at this moment it technically doesn't look much more than another faction to pew Gallic lawfuls and corporations in the Taus and Gallia, to which we already have a ton of other factions.
The following factions fit all the categories: LSF, BIS, Privateers, Maquis, Brigands, Outcasts. Maquis are rather for terrorism, LSF and BIS aren't for piracy either (rather just mere disruption of the flow of supplies), if you want to outright pirate, you can still chose Privateers, Brigands, Outcasts, from which I guess we can discard Outcasts due to your conflict mentioned in your story, and Brigands for being of Gallic origin. The result is that Privateers are still the closest to what you might want to be, but keep in mind that the conclusions I've drawn are based on the little information you've shared with us so far.