Prior to the Vietnam War, very view Vietnamese lived anywhere other than Vietnam. Some lived in France, due to the French colonial association with the country. When the French Indochinese War ended, some Vietnamese in fact relocated to France, with a small number of actually being Vietnamese who were in the French armed forces. It wasn't a large number, however, like it would come to be with Algerians.
The end of the Vietnam War however was different.
Many Vietnamese fled because they legitimately feared Communism, putting the lie to the often stated proposition that the South Vietnamese didn't really care how the war ended. Thousands did, and of those who did, most didn't make it out of Vietnam.
Over 2,000,000 Vietnamese now live in the US, with 60% of those having been born in Vietnam. 37% of them report themselves as being Buddhist, 36% Christian and 23% aren’t affiliated with any religion. Vietnamese Americans are more than three times as likely as Asian Americans overall to identify as Buddhist (37% vs. 11%), but with Buddhism being the "native" religion of the country in American eyes, that numbers if surprisingly low.
Indeed, it gives some credibility to Dr. Geoffrey Shaw's assertion in his biography of murdered South Vietnamese President Ngô Đình Diệm that at the time of the his assassination Buddhism was in significant decline.
However it would also reflect that the American understanding isn't really all that correct. While some regard Christianity as "introduced", the fact is that Buddhism is as a well, with it being Indian in origin. Vietnam also has a folk religion which shares many common elements of other Asian "folk" religions, including devotion to ancestors.
Today in Vietnam Buddhists make a 13.3% of the total population, and Christians a declared 7.6% with 6.6% being Catholic. Hoahao Buddhists make up 1.4%, Caodaism followers 1% and followers of other religions including Hinduism, Islam, and the Baháʼí Faith, representing less than 0.2% of the population. Folk religion has experienced a revival since the 1980s, and it's widely believed that the official 7.6% of the population being Christian is in error, and actually over 10% of the population is Catholic. The Catholic faith in Vietnam is so vibrant that it now supplies Priests to the United States, as the nation has a surplus of Priests itself. Looked at this way, Buddhists and Christians are overrepresented in the United States in comparison to Vietnam, but it might actually present a more accurate make up of the Vietnamese religious makeup.
Or perhaps not. One of the groups that most feared a Communist takeover in Vietnam were Catholics, and for good reasons. Catholicism has always been antithetical to Communism and in many instances it was credited with being the only effective force on the Globe opposing it. Elsewhere in the same general region of the world, some credibly credit the CAtholic Church for preventing mid 20th Century Australia from falling into Communism, something the far left in that country still strongly resents. Catholics were well represented in the South Vietnamese government and military, and interestingly some of the leaders of its military converted to teh Faith during the war or even after it.
Buddhism was introduced to Vietnam in the 2nd or 3d centuries BC, so its presence there is very old. Christianity in Vietnam is mostly the story of Catholicism there, and was introduced by the Portuguese, not the French as is so commonly assumed. Vietnam was never part of the Portuguese Empire, but its influence was very long, and very significant. The Vietnamese alphabet was developed by the Portuguese.
The Communist Vietnamese government has always been hostile to religion in general and openly repressive against some. Catholic have notably been oppressed, and the native Cao Đài religion, which originated as late as 1926, was oppressed by both the Republic of Vietnam and Communist Vietnam.
France did of course have all sorts of influences on Vietnam due to its conquest of Indochina which commenced in 1858 and ran to 1885. The very first Vietnamese refugees I met in the US spoke French as well and their native language, reflecting that they had been educated during the French colonial period. Today that number has dropped way off, with their being no need for French in daily life. A much higher percentage of Vietnamese in Vietnam speak English today than French. One of the very first refugees I met, who had been an engineer in Vietnam, but who worked as a city mechanic in the US, struggled with English, but spoke French fluently.
At one time the Vietnamese Diaspora retained a close cultural connection with the defeated Republic of Vietnam and in some places, they still do. Republic of Vietnam flags were prominent in some locations this past month in areas with large Vietnamese populations and they were displayed during commemorations of the fall of Saigon. However, there are a not insignificant number of Vietnamese now who are post war immigrants, and whose association is not as strong or there at all. The Republic of Vietnam itself is officially detested in Vietnam, and often open views about the Republic reflect the same.
Vietnamese in the US often express the hope that someday the separated people can be united somehow, something that's common for diaspora people. But it won't come to be so. As time moves on, the Vietnamese in the US will become more and more American, like Italian Americans are and Irish Americans, and less Vietnamese. Part of that will occur through intermarriage, which is occuring in the US but which interestingly was not a common occurrence during the French occupation of Vietnam or the Vietnam War, with the cultural differences at the time simply being to vast for it to arise frequently.