 If you liked
Fruits Basket
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 ...then you might like
Kobato.
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Similar naive and happy-go-lucky heroines that are Goody two shoes and only think in other´s well being.
Slice of life moments of the heroines daily lives helping/healing people around them.
Drama and Romance involving main characters and supporting characters too.
Both also have supernatural elements: cursed people who transform into animals and for a similar reason: one of them (the dog in kobato, the cat in Furuba) angered God and for that all of them were punished.
Both leads are cute, sweet, but naive girls who can be kinda dense. Both manga are very cute, with undertones of fantasy.
Fruits Basket and Kobato are two manga series with an extremely happy-go-lucky brown-haired young girl as the main protagonist. She touches the hearts of the people she meets and actually has a bit of a goal related towards the supernatural (hiding the curse in FuruBa, filling a magic bottle with healed hearts in Kobato). There are also several talking animal characters in this seemingly cute story.