Can someone explain the construction of this question?

It's an archaic construction for a question. Older grammatical forms of English tend bear more resemblance to German grammar the farther you go back. I don't know who the people are in the picture, and whether they speak in this peculiar way. Perhaps I'm missing a reference.

Did the day go well? It's the way other Germanic languages would phrase this question, and is seen in older forms of English (by the 1940s, when this photo is from, it would already have seemed old-fashioned, at least). English is rare for using 'do-support' in questions and negation. Also compare 'I didn't eat' and 'I ate not'. The latter sounds old-fashioned.

I'm afraid not, it looks like gibberish to me.

The title comes from a poem, so the unusual word order is poetic. More typically it would be “did the day go well?”

To quote wikipedia: The film was based on a short story by the author Graham Greene entitled "The Lieutenant Died Last".[3] The film's title is based on an epitaph written by the classical scholar John Maxwell Edmonds. It originally appeared in The Times on 6 February 1918 entitled "Four Epitaphs". Went the day well? We died and never knew. But, well or ill, Freedom, we died for you. "Went the day well" also appeared in an unidentified newspaper cutting in a scrapbook now held in the RAF Museum (AC97/127/50), and in a collection of First World War poems collated by Vivien Noakes.[4]

It's pretty straightforward. "Went" is the verb. "The day" is the subject. "Well" is an adverb. The verb is at the front because it's a question. In sentence form: "The day went well." You might be confused by the lack of auxiliaries. In contemporary English we would normally say, "Did the day go well?"

It's a calque from some other L1/native language that commonly uses investion to form questions. Normal English would be "Did the day go well?" Ah, I see the response from u/BobbyP27 . That makes sense. And I see the references to the poem, in which the inversion is used. So the phrase serves double duty.

The title was obtained from this: >The film's title is based on an epitaph written by the classical scholar [John Maxwell Edmonds](https://en.wikipedia.org/wiki/John_Maxwell_Edmonds). It originally appeared in [*The Times*](https://en.wikipedia.org/wiki/The_Times) on 6 February 1918 entitled "Four Epitaphs". >**Went the day well?** We died and never knew. But, well or ill, Freedom, we died for you.

To me this sounds like an English-ification of German grammar. I'm not sure what the photo is depicting or what the subject material is, but I would guess it's referencing something Germanic?

This is the title of a 1942 British film. The film was made during the second world war, and the premise is that a bunch of German soldiers, disguised as British soldiers, arrive at an English village and set up a camp, that is supposed to be in preparation for a German invasion. Small details about how the Germans behave, speak, and things they have with them, cause the villagers to figure out who they really are. The choice of "went the day well" as a title is deliberate, because it is an example of a typical mistake a German speaker makes when speaking English: the word order is natural for German, but not for English, so it fits with the premise of the film.

It’s a beautiful film, especially when you understand that it was made during the war when the threat of invasion was very real.

Looks like an awkward translation for: "Did the day go well"?

It’s German directly translated, I think

It's incorrect. I think it's supposed to be a joke.