Much like Harrison Ford, Eddie Murphy has been spending the back nine of his life reflecting on what made him great because maybe this is just what old dudes do when they feel like they’ve earned their victory laps. Ford has revisited “Star Wars,” “Blade Runner” and “Indiana Jones” in his late ‘70s/early ’80s, and Murphy, at 63, has reexamined “Coming To America” and now, a fourth “Beverley Hills Cop.” Most legacy sequels, as often dubbed, reek of cashing in again superficially, but men of these statures are often exceptionally wealthy, and so their motivations, oddly enough, are often genuine re-exploration of a character they love. Titled “Beverly Hills Cop: Axel F,” the film, despite a very baggy first act seemingly hellbent on lazy spot-the-nostalgia layups, surprisingly works. Coming together in the second half when the story actually commences, and the greatest hits indulgences are set aside, ‘Axel F,’ while seeming like a dud at first, entertains, thrills, and even feels like it holds genuine intentions.

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But again, it’s very wobbly at first. ‘Axel F’ begins in Detroit with an entire big set piece totally unrelated to the whole plot; essentially just an excuse for Murphy to cause destruction and mayhem and to reiterate to the audience: this cop has always been and will be a loose canon maverick that plays by his own rules. This action-packed but rather rote sequence also seems like an excuse to shoehorn in Foley’s constantly exasperated boss, Jeffrey Friedman (Paul Reiser), who is out the door and retiring.

The real story is, of course, in Beverly Hills, where Foley’s estranged daughter, Jane (Taylour Paige), a powerful criminal defense attorney, represents a low-level drug mule pro bono. But this case is connected to the death of some law enforcement and other shady types, and soon masked thugs threaten her life if she doesn’t drop the case. Naturally, it’s “Beverly Hills Cop” franchise sidekick Billy Rosewood (Judge Reinhold) who calls Axel to warn him his daughter is in danger.

Despite their years of disaffection and Foley as an awol dad who disappeared and caused seemingly irreparable damage, he whisks down to Los Angeles to help out his daughter, only to discover she wants nothing to do with him. Quickly arrested after some early typical Foley wrecking ball shenanigans—which puts him in the crosshairs of his old buddy, Sgt. John Taggart (John Ashton), now unretired and back on duty— Foley’s stay in Beverly Hills gets extra complicated when he discovers his arresting officer, Detective Bobby Abbott (Joseph Gordon-Levitt), is his daughter’s ex-boyfriend (“You’ve had intercourse with my daughter” he deadpan quips with humorous Murphy-like perceptiveness). Kevin Bacon also co-stars as Captain Cade Grant, a slick, smooth, and subtly loathsome detective whose Rolodex and well-tailored suits belie what should be a more modesty police officer salary.

Worse, this first act is just woefully slathered with sentimental, seemingly desperate attempts at sandwiching nostalgia in musically. Every single “Beverly Hills Cop” hit known to man is aggressively deployed in the first 25 minutes; Harold Faltermeyer’s classic synthy theme, The Pointer Sisters’ “Neutron Dance,” Glenn Frey’s “The Heat Is On,” and even Bob Seger’s “Shakedown” from “Beverly Hills Cop II.” This musical wink-wink throwback-ness is so obnoxious at first that ‘Axel F’ seems unsalvageable. Still, surprisingly, once all this nostalgic nonsense is dispensed with and out of its system— and the story finally begins— ‘Axel F’ begins to slowly entertain as it should.

Beverly Hills Cop: Axel F

The plot is slightly beside the point but essentially revolves around conspiracy and corrupt cops who don’t want that aforementioned drug mule or his attorney to discover any of their nasty secrets. But where the movie starts to gel is in its two supporting characters, Gordon-Levitt playing the new straight man, and Paige imbuing the film with even a little, dare I say, pathos.

Directed by commercial filmmaker Mark Molloy, who makes his directorial debut with workman-like efficiency, ‘Axel F’ really works best in its buddy cop rhythms and staying out of that way. When Murphy and Levitt riff with each other, and Murphy is allowed to improvise with funny R-rated intensity, it finally starts to deliver cackle and the amusing predicaments of the original films and their amusingly wayward spirit.

Amongst the laughs, the wild set pieces (one involving a helicopter is amusingly comical), and the many shoot-outs, ‘Axel F’ even manages to spend time meaningfully addressing the ideas of absentee fathers and the damage they cause, resentful children, and the challenges of forgiveness, without shortchanging the emotions or upsetting the “Beverly Hills Cop” franchise applecart.

Paige was already incredible in things like “Zola,” but she is dynamite in her role and injects the movie with a little soul and feeling; not even one beat of hers is emotionally false. Gordon-Levitt also understands his straight-man assignment and underplays it perfectly, yet still knows when to panic and freak out when Foley goes too far (a perfect stand-in for Reinhold, who is sidelined for most of the picture).

And yes, Bronson Pinchot turns up as the fabulously flamboyant Serge, and it should be eye-rolling, but his appearance does illicit some chortles and guffaws. Luis Guzmán also shows up in a small role as drug cartel boss—a relative of the drug mule who Murphy and Gordon-Levitt want to exonerate since it’ll put the pin on the bad cops— and it’s a diverting little scene reminding us how much he’s been missed on screen in recent years.

Murphy may have stumbled with the hollow and rehashing “Coming 2 America,” the exact kind of retread that ‘Axel F’ could have curdled into. Still, eventually, the comedy coalesces enough to chalk up a small win. Mind you, “Beverly Hills Cop: Axel F” isn’t reinventing the wheel, and low expectations might help. But it does make a remarkable transition from something that initially feels dire to something that eventually lights up, pleases, and produces some foul-mouthed ‘Beverly Hills Cop’ energy that feels familiar in the best sense. Now I wouldn’t push your luck further than this, but if you wanted some redemption for “Beverley Hills Cop III,” and a lookback legacy sequel that doesn’t tarnish its reputation, ‘Axel F’ is more or less the ticket. [B-]