It would probably be annexed by France, since it wouldn't be able to resist Syrian expansion on it's own, and the Christian government would rather be a part of France than Syria.
Aslo regarding demographics. In 1913 the population of the Lebanon Mutassarifate was almost 80% Christian, but more important it was 58% Maronite, in other words the Maronites could for some time have dominated the territory without opposition (which to them was important, because although the Ottomans had assigned Christian leaders to the area before WW1, they had never been Maronites). The reason more land was considered important by both the French and the Maronites was because Lebanon had suffered from a great famine during WW1 and wasn't doing well economically, said famine may have halved the population of the province (the actual numbers are sketchy).