The same way you buff activity in any faction. By having a solid core of varied activities and fluid roleplay that keeps throwing you new things so that your members are always on their toes and expecting dynamic roleplay to occur.
The GRN Royalist factions (I'll talk about the GRN in particular) have a fair bit going for them if you take the time to analyse their situation.
PvP? There's plenty available with two houses and a large assortment of smaller factions all willing and able to fight you. And you have an excellent snub line and a mostly competent capital ship line to fight in.
Trade? Some very lucrative runs are through Gallia, and in the GRN we're giving military convoys some serious thought. Trade factions like the EFL and GMS also have great things going for them in this regard, so people joining them would be helpful.
Roleplay (as in the non shooting variety?) Again, give it some thought. As a Goliath of a house, almost all factions in it's immediate vicinity are facing a real challenge, and can determine their attitude accordingly, whether to fight or flee or join... Personal character based things also have a chance, with intrigue going on both inside the house and outside it, and the House losing it's moral fibre as it descends into more and more war. (TL;DR- You can be evil.)
The house itself doesn't appeal to you? Admittedly it was a horrible mess in the last mod version but I can assure you that this mod version, significant improvements have been made and it's a very possible place to interact in. Roleplaying a french doesn't appeal to you? GRN at least, allows other nationals to join via the Foreign Legion.
If you're interested in becoming a part of it, feel free to contact either ChillerMiller, Redon, Omicega or Myself on skype and we'll be happy to answer any questions you have.