((Definitely ninjaed, by LS, but as I'd written a lot... far more than intended ...maybe it'll add
something..!))
I'm fairly sure that most films about the Korean War, from the US perspective, won't be useful suggestions at all. For various reasons.
Though the very first that comes to mind is M*A*S*H (yes, written like that). I won't link the Wikipedia page that you're not going to see, but I shall quote (parts of) its introductory section:
M*A*S*H (stylized on-screen as MASH) is a 1970 American black comedy war film [...] based on Richard Hooker's 1968 novel MASH: A Novel About Three Army Doctors. The picture [...] became one of the biggest films of the early 1970s for 20th Century Fox.
[sidebar:: Running time: 116 minutes; Country: United States; Language: English; Budget: $3 million; Box office: $81.6 million]
The film depicts a unit of medical personnel stationed at a Mobile Army Surgical Hospital (MASH) during the Korean War. [...] Although the Korean War is the film's storyline setting, the subtext is the Vietnam War – a current event at the time the film was made. Doonesbury creator Garry Trudeau, who saw the film in college, said M*A*S*H was "perfect for the times, the cacophony of American culture was brilliantly reproduced onscreen".
The film won the Grand Prix du Festival International du Film, later named the Palme d'Or, at the 1970 Cannes Film Festival. The film went on to receive five Academy Award nominations, including Best Picture, and won for Best Adapted Screenplay. In 1996, M*A*S*H was included in the annual selection of 25 motion pictures added to the National Film Registry of the Library of Congress being deemed "culturally, historically, or aesthetically significant" and recommended for preservation. The Academy Film Archive preserved M*A*S*H in 2000.
The film inspired the television series M*A*S*H, which ran from 1972 to 1983. [...] Altman despised the TV series, calling it "the antithesis of what we were trying to do" with the movie.
The film (and the TV adaptation, which most people remember) very much acted as satire on the Vietnam War, as mentioned (the Vietnam conflict ended not long after, the Korean one is still technically active!) and isn't really about the battles, etc, unlike (I presume) your film. ((Skipping back from having reviewing all noted films about the war, for a bit I write later, I'm guessing it's likely to be The Battle at Lake Changjin (2021), The Battle at Lake Changjin II (2022) or Sniper (2022)?)). I actually have no idea whether M*A*S*H (film or TV) is likely to be available to you. Or to be the kind of thing you'd want to watch anyway.
I had a quick look at what other films might interest/be available to you:
Many films, books, and other media have depicted the 1950—53 Korean War. The TV series M*A*S*H is one well known example. The 1959 novel The Manchurian Candidate has twice been made into films. The 1982 film Inchon about the historic battle that occurred there in September 1950 was a financial and critical failure. By 2000 Hollywood alone had produced 91 feature films on the Korean War. Many films have also been produced in South Korea and other countries as well.
..but:
Compared to World War II, there are relatively few Western feature films depicting the Korean War.
Of those listed, from the US, only The Manchrian Candidate[1] stands out in my mind as something I'm familiar with, which is not really "a war film". And then there's the sole mentioned British film[2], which I've either seen or seen bits of or I'm totally confusing with something else. (Though not of course "The Hill", for which I'll provide a
link for everyone else who is wondering, nor Hamburger Hill/etc.)
Really, there's not much love for the original conflict (from 'our' perspective of preventing the post-Japanese Soviet-controlled North from rolling over the post-Japanese American-controlled South, after neither local side could agree on reunification terms, but doubtless described
very differently in your circles), which just reinforced a form of the original post-WW2 division in a still tense stalemate that
was one of the few obvious remnants left of the Cold War.
In the likes of British Culture, being a Korean War veteran indicates a very narrow band of largely 'forgotten' soldiers, probably missed WW2 (by being too young), but still were part of the original wartime call-up and then had the (mis)fortune to be sent half a world away to achieve... a pause in hostilities. I know someone (a somewhat older male relative) who
didn't go, but possibly only because he wasn't rated fully fit at the time - others from his particular induction did, but I never learnt if he even knew how 'their war' went, just how his own time in uniform did. But it was a cultural tag, of sorts. (I just (re)discovered that the character Basil Fawlty was a Korean War veteran. "Killed four men". He was in the Catering Corps...)
[1] "The Manchurian Candidate (1962), adapted from a thriller novel The Manchurian Candidate (1959), directed by John Frankenheimer, and featuring Frank Sinatra and Angela Lansbury. It is about brainwashed POWs of the US Army and an officer's investigation to learn what happened to him and his platoon in the war. The 2004 remake starred Denzel Washington and Meryl Streep."
[2] "A Hill in Korea (1956) is a British war film. The original name was Hell in Korea, but was changed for distribution reasons, except in the U.S. It was directed by Julian Amyes[8] and the producer was Anthony Squire."