The Australian Official History thought that the British, Indian, and Australian troops showed a better spirit than did the Vichy French and French colonial troops. The situation was complicated by the issues regarding the campaign in France in 1940 and the French defeat, the attack on Syria and Lebanon where the French thought themselves to be morally superior to the attacking forces. The campaign was motivated, supposedly, by concerns that the Germans were using Syria for operations. The French thought that the attack was unjustified. The French fought well, at least the Australians thought so.
While the 6th Australian Division learned valuable lessons about mountain warfare in Greece, the 7th Australian Division learned their mountain warfare lessons in Syria and Lebanon. They had the opportunity to apply that knowledge in 1942 in a much different context. They had seen the importance of controlling the ridges in mountainous territory and saw the value of mortars over artillery in such and environment. They also learned how to fight tanks with guns, both anti-tank guns and field guns firing over open sights. They also gained experience with ambushes in mountain passes.
In the Syrian campaign, air power was mostly of minor importance. The exception was the battle for Palmyra, where the French air force had considerable success. An attempt to use air power at Damour had only small success due to the small numbers of aircraft that were available. The mountainous terrain also impeded the use of air power. There was the problem of finding targets on the ground for one thing. There was also considerable delay between requesting assistance and the actual arrival of aircraft. They also found that the French were very successful in concealing artillery from aircraft. The navy, however, was very well protected by aircraft against air attack. That enabled the ships offshore to provide good artillery support to land forces. This is based on the account in Vol.II of the Australian Official History.