The Merovingian bloodline, descended from Charlemagne

The elm at Gisors represented the Merovingian bloodline, and the battle was about the claim to the right to rule. Henry II was the grandson of Fulk V, King of Jerusalem. But this title was bestowed through marriage to the daughter of the previous King of Jerusalem, Baldwin, who did have a direct male succession from the Merovingian Kings. Henry II's claim to France was based on obscuring the truth; his claim to blood descent was untruthful but politically worth making if the facts could be obscured. However, in a more relevant light, his son Richard did embody a true claim, because his mother, Eleanor of Aquitaine, was descended from Charlemagne and therefore Clovis, one of the first Merovingian Kings. The Plantagenets established their Merovingian heritage only through Eleanor of Aquitaine; it was valid for Richard to make the claim (though he couldn't because he wasn't yet king), but not for Henry II - even though his grandfather had married the daughter of a legitimate lineal male descendant of the Merovingian line and thus became the third King of Jerusalem after Godfroi and Baldwin.