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Milton 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.

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. What follows is a funny, wildly inventive ride as the three neighbors find meaning and connection later in life - thanks to this unlikely stranger.—Bleecker Street

Milton Robinson is a 79-year-old widower living on his own. He frequently attends city council meetings and receives help from his daughter. One day, a spaceship crash lands in his backyard flower garden and a blue humanoid alien crawls out of it. Milton attempts to get help by calling the police and his daughter, and informing the city council.

However, all of those people believe Milton's claim is further proof of his senility. Milton treats the alien as a house guest and discovers the alien will only eat apples.

Milton's acquaintance, Sandy, visits Milton and discovers the alien. Sandy tells Milton to not tell anyone about the alien. Joyce, another elderly woman, also discovers the alien. Sandy names the alien "Jules", but Joyce wants to call the alien "Gary" (after singer-songwriter Gary Jules). Jules begins repairing the spaceship but does not appear to be making quick progress.

Milton's daughter, Denise, hears about her father's antics and schedules him for a mental evaluation, where Milton and Denise are told that Milton's faculties are quickly diminishing and that he should consider assisted living. This upsets Milton, and he angrily leaves.

Sandy, who is attempting to start a program to connect with the town's young citizens, is burgled by a young man she invites to her house. After Sandy states that she will call the police, the man tackles and attempts to strangle her; however, Jules receives a vision of the events and telepathically causes the man's head to explode. This raises the suspicion of the NSA, since they are conducting an ongoing search for the crashed spaceship.

Milton, Sandy, and Joyce realize that Jules needs seven dead cats to power the spaceship, so Milton and Sandy go out to find some, while Milton continues to be troubled by thoughts of his declining faculties. They are unknowingly followed by police, who observe their strange activities. Joyce decides to sacrifice her deaf and blind cat so they are able to repair the spaceship.

Jules invites the three to travel in the spaceship. Milton considers accepting. He receives a phone call with his daughter and appears to be hesitant. However, when the NSA kicks down Milton's door, he, Sandy, and Joyce hurriedly escape in the UFO. Jules drops them off at another location on Earth and they part ways.

Milton continues to deteriorate mentally and some time later, Jules visits Milton again.