NO, it is not finished.
The anime finished before the manga:
Anime finished: July 03, 2007
Manga finished: February 12, 2008
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Anime - Base
Release date: April 03, 2005
Anime - Sequel
Release date: April 17, 2007
Eikoku Koi Monogatari Emma tells the story of Emma, a hardworking and content maid in Victorian England. She finds herself falling in love with William, a gentleman from a newly established wealthy family.
Their budding romance faces significant challenges due to the rigid class structure of the time. Society frowns upon relationships that cross social boundaries, creating considerable obstacles for them.
The anime explores the difficulties they face as they navigate societal expectations and attempt to pursue their feelings for one another. It's a story about love challenging the established norms of 19th century English society.