Jules follows Milton (Kingsley) who lives a quiet life of routine in a small western Pennsylvania town, but finds his day upended when a UFO and its extra-terrestrial passenger crash land in his backyard. Before long, Milton develops a close relationship with the extra-terrestrial he calls "Jules." Things become complicated when two neighbors (Harris and Curtin) discover Jules and the government quickly closes in.
This modest Preston Sturges comedy stars Dick Powell as an office clerk dreaming of better things and Ellen Drew as his more pragmatic girlfriend. Powell convinces himself that his fortune will be made if he can win a slogan contest sponsored by a coffee company. Powell's contribution: "If you can't sleep at night, it isn't the coffee, it's the bunk!" Three of Powell's fellow workers decide to have some fun with him; they fake a telegram which announces that he's won the contest. The deception snowballs to the point that even the head of the coffee firm (Raymond Walburn) labors under the misapprehension that Powell has won. When the painful truth is revealed, Powell finds himself broke (because of all the creature comforts he's bought) and jobless, but at least he's retained the love of his wife. A cute deus ex machina to the story appears in the person of William Demarest, the foreman of the "jury" that is judging the slogan contest.
After a family gathering is disrupted by the sudden death of the patriarch, two detectives are sent to investigate the mysterious incident. But as the dysfunctional family continues to fight, the detectives begin to consider the idea that the death may not have been an accident.