So... is Mahou Senshi Louie finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: September 18, 2001
Manga finished: September 19, 2009
We could not confirm the source content in MangaUpdates.
Watching Order (by release date)
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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Synopsis
The anime follows Louie, a powerful but somewhat unconventional mage, who unexpectedly joins a trio of female adventurers: a thief, a fighter, and a priestess.
Their adventures take them through dangerous ruins and into battles with various dark forces as they explore the kingdom.
Throughout their journey, they encounter new people and gradually become aware of a dangerous conspiracy brewing within the realm.