It's interesting you mentioned Korea, because Vietnam was officially split at exactly the same time as Korea - during the 1954 Geneva Conference.
Before WWII, the Viet Minh led by Ho Chi Minh led an influential if embattled Communist anti-colonial guerilla movement in North Vietnam against the French. During WWII, France capitulated with Germany and the new proxy state of Vichy France assumed joint control of Vietnam together with Japan. The Japanese were overextended across China already, and the Vichy government was powerless, allowing the Viet Minh presence to grow rapidly in the vacuum. In March 1945, when Germany was rapidly losing the war in Europe, Japan deposed the entire French administration in Vietnam, replacing them with locals. Japan surrendered 5 months later, and that vacuum enabled the Viet Minh to sweep in and occupy almost everything in North Vietnam. In the South, scattered weaker groups tried to assert their position too.
France quickly moved to reclaim the country, rapidly seizing control of most the cities. In 1948, the Halong Bay agreement created the State of Vietnam, an associated state (i.e. a puppet) of France whose head of state was Emperor Bao Dai. Previously, Bao Dai had been the nominal head of Annam, the centre bit of Vietnam, while Tonkin to the north was a vassal of Annam, and Cochinchina to the South was ruled directly by the French. In practice, the French controlled everything. Local governors did most of the day-to-day administration, but were supervised by French residents with full staffs. Now Bao Dai was the nominal head of the whole country, but the situation was no different from before. In reality, the French controlled at best half of the country, and projecting power beyond the major cities was both difficult and dangerous. In the context of the Korean War happening at the same time, China and the USSR then recognised the Democratic Republic of Vietnam, and US and UK recognised the State of Vietnam.
Fighting continued until 1954, when the French were defeated in Dien Bien Phu, triggering a ceasefire. Literally the next day, the Communists submitted a proposal to the Geneva Conference to split the country into two. This was pretty strange since they had just won what was at the time the greatest modern anti-colonial victory. It appeared that the USSR/China were wary of a possible US intervention, but also that the Communists were tired after a decade of war. The French/State of Vietnam/USA were unhappy about this, but the tired French parliament triggered a vote of no confidence and brought in a much more anti-war government. In 1955, Bao Dai was also overthrown by his own prime minister, who was staunchly anti-French, and who believed that partitioning the country would be a good interlude for American support to reclaim the North. All parties except the USA and State of Vietnam signed the agreement, including a stipulation to hold a referendum in 1956. Eventually, the State of Vietnam argued that since it hadn't signed this agreement, it was not obligated to hold this referendum, and the division was accomplished.
Huynh (1971) - Vietnamese August Revolution Reinterpreted
Dolloz (1987) - La Guerre d'Indochinie Tonnesson (2010) - Vietnam 1946: How the war started
Nguyen (1985) - The Vietnamese Monarchy under French Colonial Rule 1884-1945
Young (1968) - The 1954 Geneva Conference
Waite (2013) - The End of the First Indochina War
Since you mentioned "monarchy" and "before the Vietnam War", which split are you talking about? Vietnam was split North-South from 1533 - 1592 (Northern and Southern dynasties period) and 1600s to 1774 (Trinh Nguyen period).
First split: Northern and Southern dynasties
In 1516 a guy named Tran Cao rebelled against the Le dynasty. An official named Trinh Duy San blamed the emperor for the rebellion and killed him. The emperor was no more, created a power vaccum, Le dynasty generals started fighting each other for power. Ultimately, Mac Dang Dung, the warlord from Hai Duong won and founded the Mac dynasty in 1527. But former Le dynasty generals won't give up. In 1530, they set up a puppet emperor Le Trang Tong, captured Thanh Hoa province and waged a war against the Mac dynasty, starting the Northern and Southern dynasties period. In the end, the Northern dynasty were defeated by Trinh Tung, the de facto leader of the Southern dynasty.
Second split: Trinh Nguyen period
The guy who set up the puppet emperor of the Southern dynasty was Nguyen Kim. Nguyen Kim was assassinated in 1545, his son-in-law Trinh Kiem took over. Trinh Kiem appointed his brother-in-law Nguyen Hoang (Nguyen Kim's biological son) as the governor of Thuan Hoa and Quang Nam provinces. Kiem later died, his son Trinh Coi succeeded but soon was overthrown by his step-brother Trinh Tung (see above). Due to some unclear conflict between Trinh Tung and Nguyen Hoang, Hoang decided to go back to the Thuan Hoa in 1600 (modern Vietnamese sources say it's because Trinh Kiem killed Nguyen Hoang's brother Nguyen Uong but some people dismissed this because Nguyen Uong was barely mentioned in the offical Nguyen dynasty history). Both Trinh Tung and Nguyen Hoang later died and their sons Trinh Trang and Nguyen Phuc Nguyen succeeded them. Nguyen Phuc Nguyen refused to pay taxes nor receive the official title that the emperor (controlled by Trinh Trang) granted him. Trinh Nguyen war broke out. After 45 years of fighting from 1627 to 1672, both side gave up and divided the coutry at Gianh river. The war would restart 100 years later in 1774, when Trinh Sam defeated Nguyen Phuc Thuan. But war didn't end there, multiple conflicts broke out in the next 30 years that ended in Nguyen Phuc Anh's unifcation of Vietnam in 1802
As for monarchy rule, the Mac emperors had absolute power in their controlled territory while the Le emperors had zero power