How would it be possible so that the French leave Syria and what could make them leave? Effects on the region and the relations with the other powers.
POD is 1920, but before the start of WW2.
Severe post-war unrest (perhaps an election with the radical left coming to power, followed by a right-wing military coup), followed by a Syrian revolt that drives the French out. The British might tacitly back a Syrian rebellion if they can be promised a sphere of influence in the country afterward. Ali bin Husayn al-Hashimi (the oldest of the Hashemite brothers) is still free at this point. Perhaps British support for a Hashemite restoration of the Kingdom of Syria, with arms flowing to the Druze-led rebels, would be enough to throw the French into the sea. Once they do, the Syrian rebels are going to demand a pretty free hand in reconstructing their country's government; likely that will include autonomy for ethnic minorities, especially the martial Druze, and a role for the rural notables who would be responsible for the majority of the fighting. Expect a quasi-feudal constitutional monarchy as a reluctant British client.
Effects on the region will be big. The French are going to be
pissed at losing Syria, and whoever helps the Syrians gain independence (here the British) is going to be viewed... poorly, especially if France is under a right-wing nationalist government. If the Hashemites are in charge in Syria, and they have more legitimacy on the Arab Street than OTL (due to being a symbol of Arab nationalism, albeit a conservative strain), the monarchies might survive in the longer term, especially if they can introduce democratic reforms and stand up to the Brits. Expect whatever conflict that resembles WW2 to be very different; imagine an expansionist, revanchist France against a non-Nazi authoritarian Germany, with the USSR and Britain not knowing entirely what to do...