From Here to Eternity has a "fandom" in the sense that a lot of people really like it. But it doesn't have a fandom the way Star Wars or the Indiana Jones movies do: little kids are still dressing up like Yoda and Ewoks on Halloween, but not Sgt. Warden and Robert E. Lee Prewitt.
You hear that, kids? Step up your WWII military costume game.
One way people have paid tribute to the movie and its influence is by constantly parodying its most famous scene: where Warden and Mrs. Holmes kiss on the beach as a wave breaks over them. Tons of works of art have lampooned what is possibly the sandiest kiss of all time, from The Little Mermaid to Grease to The Simpsons to MAD Magazine.
Also, according to this article from TCM, fans of From Here to Eternity have gone on to demonstrate its influence in their own creative work: Elaine's dad on Seinfeld, Alton Benes, is supposedly a spoof of the author of From Here to Eternity, James Jones.
There was a critically acclaimed 1979 mini-series based on the book/movie, and The Godfather famously suggested that Frank Sinatra might've got his part in the movie by having mafia guys put a horse's head in the producer's bed. Unfortunately, fiction is stranger than truth when it comes to Ol' Blue Eyes getting his Hollywood break.