Why go with modern France? Let's think along the lines of Ancient France/Gaul/Frankish Kingdoms!
Noun: Fanaticelts (last syll. pronounced 'kelts' not 'selts')
Name: Fanatickish Kingdom/Empire
Noun: Fanaticks (add Merolvingian or Carolingian before noun if desried)
Name: Holy Fanatican Empire
Noun: Holy Fanaticans (throwback
Adj: Fanatickish OR Holy Fanatican
Name: Fanatis (pronounced FanatEE)
And before anyone decides to remind me that the Franks (a la the Frankish Kingdom and the Holy Roman Empire) were Germans, let me say that it was France, not Germany, that ultimately kept the Frankish name.