With the Dissolution of the ottoman Empire both France and Britain gained control of Greater Syria and the Levant, They finally had control over much of the holy land, an objective of the original crusades centuries ago.
So why didnt they keep it? Did they not feel the same convictions as the crusaders? Were there no plans to create an Antioch or Jerusalem based religious area?
The British and French did keep Syria and Palestine. They maintained control for about 30 years, until a combination of anti-colonial sentiment at home, local insurgencies and economic pressure after WWII forced them to withdraw. Also, the French decision to separate Lebanon from Syria was partly due to the latter being Christian majority at the time.
That being said, the 20th century motivations were completely different to the 13th century motivation.