The “Law & Order” franchise may steal from gory headlines, but by the end of most episodes, the carnage is neatly mopped up and the robotic detectives return to their pods in Westworld. As junk food goes, it’s beef jerky.

I’d like to report that “Shots Fired,” premiering Wednesday on Fox, is prime rib. It’s not, but the 10-part series comes close at times, thanks to a fierce performance from Sanaa Lathan and subtle directorial touches.

The story opens seconds after a deputy (Mack Wilds) in a sleepy North Carolina town kills a teenager during a routine traffic stop. The cop is black; the teen is white.

The circumstances trigger interest from the U.S. Department of Justice, represented by an ambitious young black prosecutor, Preston Terry (Stephan James), whose cockiness would get him canned anywhere other than a prime-time soap opera, and investigator Ashe Akino (Lathan). A female version of Mel Gibson’s “Lethal Weapon” character Martin Riggs, she’s riddled with guilt over a police shooting years ago. The friction/friendship between the mismatched partners is one of the best things “Shots” has going.

Creators Gina Prince-Bythewood and Reggie Rock Bythewood hope to spark a conversation about race relations and police corruption in modern-day America, but fall short. The case, which somewhat inexplicably incorporates the underreported death of a black teenager, is a bit of a yawner — the real-life twists and turns in the death of Michael Brown in Ferguson, Mo., are far more compelling. And the No. 1 suspect in the black teen’s death, a rich businessman who wants to build a mega-jail, is nothing more than a country-fried caricature. He’s played by Richard Dreyfuss, who seems to have picked up his accent from binge-watching “Designing Women.”

In terms of generating debate at the dinner table, the Bythewoods can’t hold a candle to the third season of ABC’s “American Crime,” also set in North Carolina.

“Shots” works best when it steps off the soap box and takes a street-level perspective. In one of the most moving moments of the first six episodes, the grieving mothers of the two slain children are chauffeured separately to a talk-show appearance, the radio blaring news reports in each vehicle. The white mother orders the limo driver to turn it off. The black mother clearly wants to do the same, but stops herself — she’s been conditioned not to make such requests. It’s a quiet but effective statement on privilege.

In another scene, oily Sheriff Platt (Will Patton) teaches Terry a lesson by pulling over a white family on the highway and ordering the prosecutor to frisk the suspects. Nothing shocking happens, but the scene is more tense than a four-car chase.

And then there’s Lathan. The actress seemed poised for stardom after a breakout role in 2000’s “Love & Basketball,” created by Prince-Bythewood, but never got another opportunity to showcase her depth and talent. This is finally it. Her Akino is a hard-drinking, seductive, volatile mother who lets her daughter’s nanny know she doesn’t appreciate her enforcing bedtime by hurling a vase near her head. She’s also vulnerable, especially when threatened with separation from her child.

It’s the kind of performance that makes you wish “Shots” was firing on all cylinders. The fact that it’s only occasionally on target will have to suffice.