I just can't believe it.

Then here's what it says from the website.
Why are none of the villagers aware of an enchanted castle only a relatively short distance away from where they live? Part of the Enchantress's curse not only seals the castle off from the outside world, but makes everyone in the surrounding area forget all about it.

The confusing timeline of the seasons in the animated filmnote  is explained here by having the castle — on top of everything else — be locked in an eternal winter, while it's clearly summer in the world outside.

The puzzling implication that the Prince was left to run his castle at only 11 years old — "Ten years we've been rusting" since everyone was transformed, but the rose blooms until his 21st year — is eliminated by dropping all references to his age and how many years pass before Belle comes to the castle, and firmly establishing that he was an adult when he was cursed. "Ten years" is changed to "Too long". In the meantime, a Flashback to his youth has his parents appear.

Belle and Maurice are given significant Backstory explaining why they moved to the village in the first place ("Every morning just the same/Since the morning that we came/To this poor provincial town") and why Belle has a Missing Mom. They lived in Paris until a plague killed Belle's mother. Maurice became desperate to protect Belle and thus they moved to the small, safe village. This also provides an alternate reason for Maurice setting out in the first place; his music boxes are sold at an out-of-town market once a year. This same change explains better why Belle is an outcast in the village, as they see her as a city-born kook obsessed with reading (something only the well-educated do).

Gaston is a war hero on top of having good looks and hunting/fighting skills, which goes further in explaining why someone so obnoxious is so beloved and trusted by the townsfolk. Mentioning a war in his introductory scene also quickly establishes that, unlike the original hunter of animals, this one has likely killed humans before (and a Black Comedy scene where Lefou calms him down by reminiscing about war builds on this), making it a smaller jump to his evil acts later in the film.

A new conflict between Gaston and Maurice is added to the story. In the film, Maurice outright refuses to let Gaston marry Belle (in the original film, he's genuinely open to the idea of the two of them getting together, at least at first). This is what pushes Gaston to knock the old man out and tie him to a tree in the woods, leaving him to die in the cold (or to be eaten by the wolves). After he's saved by Agathe, Maurice returns to the village to confront Gaston, only for the latter to turn the tables on him by getting him incarcerated, thus sparing himself from any consequences for his crime.

The original film made it clear that Belle had no interest in Gaston and that his Stalker with a Crush attitude made him dangerous, but said nothing about the vulnerability of a single woman during that period of history. The new film has Gaston's unsuccessful wooing of Belle include him drawing her attention to the miserable life of spinsters in a peasant town once their fathers have died, making it clear to young viewers that Belle's situation isn't as easy as simply saying no.