Short answers, pulled from the story.
France was assigned the League of Nations mandate for Syria on the 29th of September 1923. The mandate lasted until 1946, when French troops withdrew from Syria and Lebanon, both of which had declared independence during World War II.
The Battle of Maysaloun was the decisive military confrontation that ended Arab rule in Syria and imposed the French Mandate. Syrian forces under minister of war Yusuf al-Azma, composed of remnant Arab army troops, Bedouin horsemen, and civilian volunteers, met 12,000 French troops under General Mariano Goybet. The French won in less than a day, al-Azma died on the battlefield, and General Goybet captured Damascus on the 24th of July 1920.
France divided the mandate into six states: Damascus, Aleppo, Alawites, Jabal Druze, the autonomous Sanjak of Alexandretta, and the State of Greater Lebanon. All were established in 1920 or 1921, and the divisions were designed partly on sectarian demographics and partly to weaken Arab nationalist movements.
France created Greater Lebanon as a safe haven for the Maronite Christian population of Mount Lebanon, which had enjoyed varying degrees of autonomy under the Ottomans. General Gouraud proclaimed the State of Greater Lebanon at a ceremony in Beirut on the 1st of September 1920. To make it a viable state, France added predominantly Muslim regions including areas corresponding to North Lebanon, South Lebanon, the Biqa Valley, and Beirut.
The Sanjak of Alexandretta received a special administrative regime under the French-Turkish treaty of the 20th of October 1921. In 1938, the Turkish military entered the province and expelled most of its Alawite Arab and Armenian inhabitants. A French-Turkish treaty was signed on the 4th of July 1938, the sanjak declared itself the Hatay State on the 2nd of September 1938, and following a referendum in 1939 it became a Turkish province.
The American King-Crane Commission, arriving in Syria in June 1919, visited 36 major cities and met with more than 2,000 delegations from more than 300 villages, receiving more than 3,000 petitions. Their findings confirmed that Syrians opposed the mandate and the Balfour Declaration and demanded a unified Greater Syria encompassing Palestine. Both Britain and France ignored the commission's conclusions.