Even thought I think there is place for straightforward "+10% Influence" LT in game, ever since the Kill count got added to the game, I can't shake off the idea it is perfect oportunity for the Franks to get some more unique and flavorful LT: Chansons de Geste!

Flavour: The epic songs about great knight/chevaliers and their magnificent deeds, something that started with Frankish trubadours and spread through whole Medieval Europe (pretty Aesthetic stuff right? some srong osmosis' here). Something that connects both aeshetic and militaristic side of Franks.(https://en.wikipedia.org/wiki/Chanson_de_geste)

Mechanics: +X Influence per Kill count on each Unit per turn and +X (like 10-50) Influence per Victory in battle; if not strong enough, could be coupled with small base +X Influence on each unit (with or without Kills) or even small +X Influence on Garrison

Imagine the Main Battle Tank braging: I might be the rusting souless machine now, but when I was young boy clad in shining armour, I slayed the Saracens and dragons first thing in the morning... BAM +50 Influence per turn!

Please let me know what y'all think, I'll be happy to fight for my idea and win... or die trying, like Roland the Brave did!