Anne doesn't really "fall" for Gilbert Blythe. They sort of grow into a love for each other. Gilbert makes no bones about being in love with Anne, but she is determined to be a self-reliant single woman. It is only when Gilbert gives up hope for a relationship with her and becomes engaged to another woman that Anne finally realizes that she loves him too. All sorts of events get in their way, but they do eventually end up together.
The miniseries "Anne of Green Gables" and "Anne of Avonlea," with Colleen Dewhurst and Megan Fellows, are the best adaptations of these books. The final scene of "Anne of Avonlea," with Anne and Gilbert on the bridge with Anne accepting his proposal is one of the most romantic scenes in any movie!
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Gilbert Blythe o_O
The boy's name is Gilbert Blythe.