If there’s one thing any film fan should take away from “Leap of Faith: William Friedkin on ‘The Exorcist,'” it’s exactly the same thing you should take away from “Friedkin Uncut,” the earlier doc about the quintessential hotshot Hollywood director of the ’70s.

The man can tell a story. And how. William Friedkin weaves anecdotes about “Exorcist” stars Max Von Sydow and Jason Miller and folds in stories about the great composers Bernard Hermann and Lalo Schifrin, both of whom he rejected when it came to scoring the film.

“I wanted a piece of music” he says, that felt “like a cold hand on the back of the neck.”

“Tubular Bells” by Mike Oldfield would do.

He rejects the notion that he was “foreshadowing ANYthing” in the iconic demonic possession thriller. Friedkin talks about “serendipity,” and “instinctive” choices, quotes the great Fritz Lang about how relying on those “accidents” and coincidences and gut feelings is “a kind of sleepwalking security” for filmmakers like Lang (whom he interviewed for a doc in the ’70s) and himself.

He recalls using an on set gun shot to get the right shocked/startled reactions from his actors.

He tells of visiting a zen garden in Kyoto when premiering the film in Japan, wondering “What the hell’s THIS about?” and then weeping at the rocks in a sea of “raked sand.”

And he declares that “It looks like, in retrospect, that I knew what I was doing.”

He did. A notoriously “volatile” figure on film sets, he’s aged into a movie making/film history/art history raconteur of the First Order, a Peter Bogdanovich, Oliver Stone or Orson Welles lite.

Friedkin sits down with filmmaker Alexandre O. Philippe to break down, deconstruct and remember “The Exorcist,” revealing his “subliminal” tricks with sound and one-to-five frame glimpses of ghostly images inserted, the people he hired or wanted to hire, from the aforementioned composers to actor Stacy Keach (who would’ve been GREAT as the younger priest) and the “influences” he recognizes, from Hitchcock’s “Psycho” to Dreyer’s “Ordet.”

But Renais (“Last Year in Marienbad,” “Hiroshima Mon Amour”) and Welles (“Citizen Kane”) were on his mind, too.

He praises the cameraman Ricky Bravo, who “followed Castro through the jungles and into Havana” as a documentary/news photographer, and who roamed Friedkin’s sets, shooting hand-held to give movies like “The French Connection” and “The Exorcist” immediacy and energy.

And he talks about art and artists, from Vermeer, Rembrandt and Pollack to James Ensor, Magritte and Caravaggio, with a nod to the great photographer Henri Cartier-Bresson, all of whom impacted how he framed shots and lit human faces.

He takes credit for restoring the Iraq prologue to “The Exorcist,” bringing his camera and star Max Von Sydow to an actual archeological dig in Al Hadhar, a sequence so beautiful Spielberg repeated it for “Raiders of the Lost Ark.”

The guy is urbane, cosmopolitan and artistically sophisticated, and while there is no peer to Orson Welles as director/raconteur, Friedkin is no slouch and a fascinating character to listen to.

No, he’s not an unimpeachable narrator in telling his own story. He gives himself the credit for taking on William Peter Blatty’s novel (Blatty chose Friedkin, not the other way around). And his Bernard Hermann story is funny, but makes him come off smarter and funnier.

Hermann’s story is Hollywood legend, and probably the true version of how the great Welles and Hitchcock collaborator snarked himself out of scoring “The Exorcist.”

And Friedkin’s ready supply of references and recollections is so impressive as to make one wonder how much of this is scripted, polished and rehearsed. Is anybody this witty off-the-cuff?

But that takes nothing away from this Friedkin appreciation, essay and “How I made that movie” documentary. He’s a genuine character, and his stories make it plain why he’s a favorite “An Evening With” guest of film festivals. On celluloid or in person, Billy Friedkin’s still a great storyteller.

MPA Rating: unrated, graphic horror violence, profanity

Cast: William Friedkin

Credits: Written and directed by Alexandre O. Philippe. A Shudder release.

Running time: 1:44