Yes the label does make sense, especially in taking over a French colonial war in South East Asia.
I'm afraid you've got that wrong. The French lost that war and gave up their colony. The US wasn't trying to take over South Vietnam and make it a colony. The US was helping South Vietnam avoid being taken over by communist military forces loyal to North Vietnam. Australia participated in the military mission during the Vietnam War, as it had in the Korean War.
A few details about Korea you left out.
The Korean War, 1950-1953
. As the war drew to a close in August of 1945, two U.S. army colonels (one of whom, Dean Rusk, would later become Secretary of State) proposed that the Soviet Union take responsibility for accepting the surrender of Japanese troops in the part of the Korean peninsula north of the 38th parallel, whereas U.S. troops would receive the surrender south of that line. This decision resulted in the division and separation of many villages along the 38th parallel and families with ties across that line. The postwar planners had intended that the division between North and South Korea would be a temporary administrative solution. After the war, the United Nations agreed to oversee elections in the North and South in 1947 in the hopes that it would lead to the reunification of Korea under a democratically elected government. However, the Soviet Union blocked the elections in its section and instead, supported Kim Il Sung as leader of the Democratic People’s Republic of Korea (DPRK). In the South, the United States supported Syngman Rhee as the elected leader of the newly founded Republic of Korea (ROK). Both Kim and Rhee were nationalists dedicated to the idea of reunification, although each ruled with a different ideological vision. In 1949, under a UN agreement, both the Soviet Union and the United States withdrew their military forces from Korea, but both left large numbers of advisors on the peninsula. The two sides were to continue negotiations over elections to reunify the country, and although the United States preferred that the resulting government not be communist, in 1949 it was still not prepared to commit militarily to preventing that outcome. Both sides periodically instigated skirmishes across the 38th parallel, but the war formally began when the DPRK crossed the demarcation line and attacked the ROK on June 25, 1950. Both Korean governments had been adamant about reunifying the peninsula, and the Soviet-supported DPRK saw an opportunity to do so with a swift strike.
As to the line for the US Marine Corp hymn you quote, it notes places they fought, not territories added to the United States.