I just finished watching Kumiko the Treasure Hunter, about a woman who thinks that the movie Fargo is real and obsessively studies it trying to figure out where the lost money is located. Anyone got examples of other movies that center around another (real) movie?
(As I’m typing this, I remembered a Jennifer Aniston movie centering around The Graduate. Really about the book, but there is the movie too, so I’ll count it.)
Are you also interested in documentaries like Hearts of Darkness, or movies about movie making like Saving Mr. Banks?
I don’t mind the tangents but I’m mainly thinking of a fictional movie that concentrates on the story of another fictional movie.
The French Lieutenant’s Woman? Jeremy Irons, Meryl Streep?
I assume we’re skipping various parodies like Airplane! and Young Frankenstein.
There’s Play It Again, Sam, an early Woody Allen movie where he plays a character obsessed with Casablanca.
“Son of Rambow” is about two kids making their own version of “First Blood”.
Off the top of my head :
Sullivan’s Travels is about a writer working on a film called “O Brother Where Art Thou.”
Singin’ in the Rain is about a studio making the transition to sound.
Truffaut’s Day for Night is about the making of a fictional film, “Je vous presente Pamela.”
Ed Wood is largely about the making of an actual film, Plan 9 from Outer Space.
Postcards From the Edge is about an actress struggling with addiction while working on a film.
State and Main is about a film crew that invades a small town to make a fictional movie called “The Old Mill.”
Argo is a docudrama about the real-life plot to extract the hostages from Iran by posing as a film crew making a film called “Argo.”
The recent The Disaster Artist is a fictionalized version of the making of one of the worst movies of all time, The Room by Tommy Wiseau.
Singing in the Rain
Buster Keaton’s 1928 silent, The Cameraman
The Stunt Man
The Player
The Artist
Of course, there’s no shortage of lists of movies about movies, although not all of them are about making a specific movie, which I think is what the OP is looking for.
Den of Geek’s 25 best movies about making movies.
8 1/2,directed by Federico Fellini
Chaplin, with Robert Downey playing the titular role
The Stunt Man, concerning a guy on the lam who stumbles into a job as, well, a movie stunt man
Hooper, one of Hal Needham/Burt Reynold’s lesser works. Burt likewise plays a stunt man.
“Sleepless in Seattle” is about a woman who is inspired by the movie “An Affair to Remember” to meet a guy at the top of the Empire State Building.
In the same vein as Hearts of Darkness is Burden of Dreams, about Werner Herzog’s obsessional making of Fitzcarraldo in the Peruvian Amazon.
I’m surprised that no one has mentioned RKO 281, a fictional portrayal about Orson Welles’ difficulties in distributing Citizen Kane due to William Randolph Hearst’s machinations.
Baadasssss! has Mario Van Peebles recreating his father Martin Van Peebles’ making of Sweet Sweetback’s Baadasssss Song.
Adaptation is primarily about screenwiter Charlie Kaufman trying to adapt Susan Orlean’s nonfiction book The Orchid Thief into a film under contract but instead ending up writing the (mostly fictional) movie the viewer is watching; it does, however, have a brief segment with a couple of scenes set making Kaufman’s previous screenplay (Being John Malkovich) into a film.
Be Kind, Rewind is about video clerks who accidentally erase all of the VHS tapes in their store and recreate the movies by filming themselves in the role.
There are, of course, a lot of films about the making of fictional movies such as 8-1/2, Bowfinger, The Player, Tropic Thunder, State & Main, *Hail, Caeser!*et cetera. However, my favorite fictional film about the film industry is Barton Fink, which is exactly what it is like to try to write for the entertainment industry. Exactly.
Stranger
The movie Hitchcock focuses almost entirely on the making of Psycho.
I would add to that list Hearts of the West, Boogie Nights, and Zack and Miri Make a Porno.
If (and it’s a big if)… IF you grant the fantasy that Tom Stoppard wrote one of his famous works after seeing a Hamlet movie, then the movie Rosencrantz and Guildenstern Are Dead is a movie (containing a play) of a play about a play about a movie of a play containing a play. 
I feel like flipping a coin.
In the movie All That Jazz The character of Joe Gideon is working on thinly veiled productions of Bob Fosse’s real life productions of the movie Lenny and the Broadway play Chicago
I always thought it was interesting how Fosse decided to make an autobiographical movie and kill off the main character.