So... is Ristorante Paradiso finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: June 25, 2009
Manga finished: January 07, 2009
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
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
Nicoletta, abandoned as a child, journeys to Rome seeking revenge on her mother, Olga. She intends to disrupt Olga's new life, but her plans are unexpectedly complicated when she discovers Olga works at a unique restaurant.
This restaurant, Casetta dell'Orso, is staffed by older, charming gentlemen. Nicoletta finds herself captivated by their warmth and the restaurant's atmosphere, challenging her initial desire for vengeance.
Instead of enacting her revenge, Nicoletta becomes immersed in the daily life of the restaurant and the lives of the people who work there. She experiences a sweet and unexpected romance, causing her to reconsider her original intentions.