In “Danny Collins,” Al Pacino, shambling along with much the same tired gait as the character he played in “The Humbling” but far more animated when thrust into performance mode (whether on stage on not), plays an over-the-hill rocker regaling audiences of sixty-something nostalgia buffs at arena events. It’s an audience of like age and inclination that will find Dan Fogelman’s utterly predictable but reasonably engaging movie, very loosely based on a real incident, most enjoyable.

The incident involved a letter written by John Lennon to British folk singer-songwriter Steve Tilston in 1971 after reading that Tilston was worried that fame and wealth might prove corrupting. The letter was never delivered, and Tilston became aware of it only in 2005. Fogelman takes that story and fictionalizes it in spades, presenting Collins as the geriatric rocker par excellence, a hedonist who dyes his graying hair and puts on a corset to endlessly repeat one-time signature hits like “Hi, Baby Love” on lucrative tours while enjoying off-stage the pleasures afforded by booze, drugs and a succession of young wives, the latest being Sophie (Katarina Cas).

In the course of a massive surprise birthday party thrown for him by Sophie, Danny’s presented with the ultimate gift by his long-time manager Frank Grubman (Christopher Plummer, reveling in the character’s cynicism): a letter Lennon wrote him after reading an interview the young Danny (Eric Schneider) had given at the beginning of his career. Lennon sent the missive to the interviewer, who pocketed it for himself, but Frank tracked it down, and it proves a life-changer for Collins, who turned to performing jaunty pop tunes penned by others rather than following his own inspiration after one of his albums flopped. Now, inspired by Lennon’s admonition to stay true to himself, he’s determined to reform, sending Sophie packing with her much younger lover Judd (Brian Smith) and taking off for New Jersey, where he plans to look up the son he’s never known, Tom Donnelly (Bobby Cannavale), the result of a brief encounter.

One strand of the ensuing story deals with Danny’s efforts to connect with Tom, a contractor with a pregnant wife (Jennifer Garner) and ADHD-stricken daughter Hope (Giselle Eisenberg) who angrily rejects the old man as too little, too late. Needless to say, Danny’s persistence eventually pays off, especially after a secret about Tom comes out. The other involves Collins’ stay at the Hilton hotel where he takes up residence intending to start writing real songs again. While acting as matchmaker between valet parker Nicky (Josh Peck) and comely clerk Jamie (Melissa Benoist), he strikes up a relationship with Mary (Annette Bening), the hotel manager and recent divorcee who initially resists his charms but gradually warms to his desire for redemption.

Fogelman manages a couple of twists in “Danny Collins” that might catch you unawares, like the outcome to the little gig that Frank arranges for Danny to perform his new material (though he fact that, as far as one can tell, he’s only written one song makes the whole thing implausible). Otherwise, even when he throws in a turn that (like Tom’s secret, or Hope’s ADHD) is meant to come as a surprise, it comes off as formulaic stuff that would barely pass muster in a network telefilm. (The very name of the darling little girl falls like a sledgehammer, especially since it’s endlessly reiterated.) For the most part, moreover, the script follows a narrative path in which one can see the stops well in advance, and in lesser hands the result would have been deadly.

That “Danny Collins” winds up being as pleasant as it is results largely from the cast. Pacino, seemingly refreshed by decent writing after the debacle of drek like “Jack and Jill” (certainly the nadir in a distinguished career), seems to be genuinely enjoying playing this larger-than-life fellow while curbing the inclination to go too far with him; and his engagement proves infectious. Cannavale and Garner make an appealing middleclass couple, and though Tom’s turnaround regarding Danny can’t escape being all too easy, Cannavale pulls it off;, while Peck and Benoist manage to bring a measure of reality to what are really sitcom subsidiary characters. Best of all are Plummer, who tosses off Frank’s gruff observations with perfect timing, and Bening, who actually makes Mary’s officiousness charming simply by flashing a toothy grin.

Fogelman strains too hard to come up with a quirky but satisfying closing note for the picture, and the footage of Tilston during the closing credits seems rather arbitrary, even if he does get a “consultant” credit (after all, the pattern of Danny’s life hardly mirrors his own). Still, while Fogelman’s script is extremely calculated and heavy-handed, the cast’s nimble execution turns it into an agreeable way to pass the time.