This cannot be easily done-
Here's a couple answers-
Answer #1 - Vietnam becomes more deeply enmeshed with USSR and Central European Communist states via Warsaw Pact, COMECON, party caucuses and other functional organizations. The Vietnamese guest worker population in East Germany, Czechoslovakia and Poland is larger than OTL. There's an internal Vietnamese Community Party rift over glasnost. Some version or other of a Vietnamese Vaclav Havel emerges and has a suitably heroic background as a veteran. The hardliners overplay their hand and lose support and the reformist party opens up to competitive elections in 1989-1991 era.
Answer # 2 - The Tiananmen demonstrations of '89, or the earlier democracy demonstrations of 1987 cause the overthrow of the Chinese Communist Party power monopoly in China by the late 80s, early 90s. The loss of any functioning model for a successful communist political system in China or Russia has knock-on effects, leading to the Vietnamese party surrendering its monopoly of power.
Answer # 3 - US led ground intervention occurs after Dien Bien Phu, and Chinese Communists do not counter it with a large overt force. US helps install anticommunist regime, possibly the Diem regime, through a lengthy, messy counterinsurgency. This reduces the communists eventually down to a small guerrilla and terrorist level. The Diem or alternate anticommunist regime in Vietnam spends a few decades as an authoritarian state. By the late 80s, early 90s, it has its first democratic transitions of power as the military steps out of politics.
Answer # 4- Sino-Soviet War occurs in 1969, resulting in massive nuke damage of China and its infrastructure and some damage to the USSR, with some of it substantial in the Soviet Far East. (Maybe such a huge war is "WWIII" and violates the OP, although I am positing that the US and its allies do *not* become military participants)
This Sino-Soviet circular firing squad is devastating to the global prestige of Communism.
The US, with bigger problems to worried about, and being tired, draws down from Vietnam. But North Vietnam, denied military aid, receives much humanitarian aid from Europe in dealing with knock-on effects of radioactive fallout and refugee movements.
Lengthy negotiations begin in Vietnam over peace and unification is brought into the agenda by multiple parties. Warfare that does continue is at a lower, guerrilla level of intensity, with neither side gaining much confidence from large conventional arms deliveries. Eventually this resolves into coalition government and an opening to participation by multiple political groups beyond simply the Communist party.
# 5 -Due to a series of rapid political failures first by the Diem regime and then its successors in the southern zone of Vietnam in the years 1954 to 1956, Eisenhower and Dulles decide that South Vietnam is a lost cause and make Thailand their first line of defense in Southeast Asia, while they allow a process of elections and political negotiations to result in Vietnamese unification. Vietnam is soon de facto controlled exclusively by the communist party from Hanoi. Vietnam begins a process of socialist construction in the 1950s through late 1970s instead of having wars. With the Sino-Soviet break, and the lack of a war with the US, early unified communist Vietnam has much tighter ties with the USSR and East Central Europe than China.
By the late 1980s, with Vietnam as a more "normal" developed Communist state, some limitations of the model are becoming apparent.
Although the cult of Ho Chi Minh and the Viet Minh resistance to France has some devotees and helps party legitimacy, this cult and legacy does not receive any reinforcement or refreshment by continued wars in the 1950s, 1960s and 1970s. The Communist Party in Vietnam is judged much more on its economic record than by its founding glory by the time we reach the late 1980s. Dissidence grows in Communist Vietnam as it does in Communist Europe and Mongolia, and it receives a more sympathetic hearing by the populace and elites as we get to the late 1980s. With the last war having ended in 1954, hardliners attempts to link reformism and dissidence to "French and American plots" fall fairly flat. Additionally, the unification by election in the 1950s gives the idea of elections more political legitimacy among communist and non-communist Vietnamese, that the dissident movement (some led by students and intelligentsia, others perhaps led by Buddhist and or Catholic or syncretic clergy).
I think honestly, that odds are at least 10 to 1 against all these scenarios, but these ideas are the best I can do with a post Dien Bien Phu p.o.d.