Lebanon as a French Overseas Department?

This may be completely ASB. But I was looking at old threads about Lebanon the other day, and I wondered if this is remotely plausible:

Upon the French assuming control of Syria, in OTL, the French greatly expanded the Mount Lebanon Christian district to form "Greater Lebanon" then made it into a separate state. What if they had enlarged it less ambitiously, so that it only today consisted of roughly the modern-day Mount Lebanon governorate and Beirut and annexed it directly to France as a département-d'outre-mer?

It might have made for a more stable environment, with a large Christian majority linked directly to France (its longtime patron). The largely Shi'a and Sunni regions, such as the Bekaa Valley, would have remained part of Syria. Of course, the Maronite Church's administrative role would conflict with French laïcité, but Alsace-Moselle has unique laws in that regard and something similar could potentially have been implemented.

Is this plausible or completely ASB?
 
ASB, because it would trigger an immediate international response and totally deteriorate France's perception throughout the world, as Lebanon and Syria were supposed to be LoN mandates, thus achieving independance ASAP. Even if they did, France had no interest in the Middle East, as they experienced powerful revolts as soon as 1920, if not 1918...
 
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