This is very unclear term.
The classic term should be French or Italian people who have lived in East Mediterrenean since Ottoman period.
but sometimes all Ottoman Europe origin people of Ottoman Empire get in this category. Even non-Catholics
In Egypt, it means different things. Ancient Christian people who came form Syria-Lebanon (Levant) are also Levantine.
In Cyprus, I think they call them just Latin, not Levantines.
What about Greece? Which country is the northest point of them?
What is their world population?
what about Italian Levantines and Italian Lebanese? Do not Italian Lebaneses call themselves Levantine? Do they lost their Levantine identityduring the French rule in Lebanon?
It seems this term just use for Turkey now.