“June Zero” is, to paraphrase Franklin Delano Roosevelt, a day that will not live in infamy. The chief image accompanying the new film by director and writer Jake Paltrow is a group of school boys eagerly huddled around a magazine. It’s a scandal sheet: The color is a lurid red, the type is humongous and the photo on front is of a topless woman whose breasts are nominally censored by two black stars. On the back cover is the photo of a dapper man in Nazi regalia, Adolph Eichmann. We are in Israel, 1962.

Mr. Paltrow states that this magazine — from all appearances, an amalgam of the National Enquirer and a third-tier variation on Playboy — was based on an actual publication. On the day of Eichmann’s execution, the editors made a concerted effort not to list the actual date lest it become a day of commemoration for those sympathetic to the Nazi cause. “June Zero” centers on the execution and the myriad events leading up to it.

Yet not on Eichmann himself. We see the man, but never full-on. Like the movie’s telltale journal, Mr. Paltrow doesn’t want to valorize a monster. Eichman was among the primary architects of “the Final Solution” and a man who almost got away. After having been captured by the Allies in 1945, Eichmann escaped and spent three years scuttling undercover in Europe. Going under the pseudonym Ricardo Klement, Eichman ultimately arrived in Argentina — which is where he was apprehended by Mossad in 1960. 

The trial in the Jerusalem District Court began on April 11, 1961. The guilty verdict against Eichmann for crimes against humanity and 14 other charges came four months later. The execution was put into motion, but complications ensued.

So begins “June Zero,” a film in which history is presented in a kaleidoscopic fashion. Mr. Paltrow takes us to the periphery of events, albeit with characters who have (or will) become vital players in this tale of meting out justice. What the picture lacks in cohesiveness and rhythmic surety is mitigated by what can only be dubbed righteous didacticism. The picture connects.

Among the significant challenges facing the Eichmann execution is how to dispose of the body. The Israelis are adamant that the remains not become a potential site of pilgrimage. Cremation is suggested, but difficult to imagine: Jewish law forbids desecration of the human body. The government contacts a factory that manufactures baking ovens or, rather, its owner, Shlomi Zebco (Tzahi Grad), uses back channels to secure the contract. The irony inherent in this means of disposal is not lost on Zebco. Indeed, he relishes it.

Zebco is a great character — abrupt, brash, and a bit outside of the law — but he’s ancillary here. “June Zero” pivots on a 13-year-old Libyan immigrant, David (Noam Ovadia); the Moroccan guard responsible for overseeing Eichmann’s imprisonment and execution, Haim (Yoav Levi); and an investigating officer of the trial, Micha (a perpetually haunted Tom Hagi).

Of all the characters, Micha is given the most thorough backstory. He’s a Holocaust survivor and the stooge of a delegation from America. Or, at least, that’s the opinion of Ada (Joy Rieger), a representative of an Israeli commission. She doesn’t want to see Micha exploited. In a moving, if somewhat anomalous, moment Micha explains to Ada why she should mind her own business. We can’t help but cheer him on. 

“June Zero” ends on an odd fillip in which we meet an older David in the here-and-now for reasons that have everything to do with historical accuracy and little with cinematic imperative. Mr. Paltrow isn’t the first filmmaker to needlessly iterate his thesis when he’s already done so to convincing effect. Explication invariably betrays a lack of trust in the audience. Still, if Mr. Paltrow errs on the side of overstating a moral lesson, he’s done a yeoman’s job of filling out its parameters.