According to the book "Lawrence in Arabia" by Scott Anderson the French government was very adamant about ending the war in control of Syria. Is there any specific reason (aside from colonization) they wanted Syria in particular(cultural reasons/ resources/ect)?
France had a long standing interest in the Maronite Christian community in what is now Lebanon, but was then part of Greater Syria. They were their international patrons during the latter years of the Ottoman Empire. As Catholics, not exactly Roman Catholics but in commune with the Holy See, they gave the French a justification for competing with the Russians for influence in the region.
In case you didn't know, the Russians claimed patronage of the Orthodox Christians in the Ottoman Empire.