Shrek

Close examination of canonical Shrek offerings reveals that Fiona was 7 years when placed in the Dragon's tower (on Christmas eve). She was 23 when Shrek rescued her. The year was 1486.

Yes, the Shrek series can be dated! Obviously, anachronisms abound in the Shrek series. But, they are placed there purposely to bring together fairy tales characters (The Little Mermaid and Pinocchio are very recent, for instance) and parody and/or commentary of modern life. To the best of my knowledge, there are no accidental anachronisms in any of the movies (no potatoes or tomatoes). Architecture, clothing, artwork (seen in the background), and written English text in Farquad's realm and Far, Far Away are all authentically late 15th century.