Period Fic

A Period Fic usually takes the characters of any fandom and places them in a different time period than the setting of the story. It may involve time travel, but most of the time it doesn't. It's akin to a Period Piece, but combined with either Fish Out of Temporal Water or reusing characters as in the Star System.

May or may not include the Used Future.

Not about averting No Periods, Period.

Examples of Period Fic include:

Rendezvous With Fate by iCe relocates Ranma ½ to feudal Japan, and casts Akane as the time-traveling widow of Ryouga, who has accidentally come back in time and possessed the body of Ranma's estranged wife, Kodachi.
Golden Day by Gondolier moves the plot of Phantom of the Opera to Hollywood in the Roaring Twenties—with good period research, no less.
Starting a year or so ago^[when?], there was a sudden explosion of Cartman/Kyle South Park fics set in Nazi Germany, with Kyle in a concentration camp, hiding in Stan's family's attic, or otherwise persecuted, and Cartman as a sadistic Hitler Youth.
Scion: The Last Aeromancer is a story on Fanfic.net which turns Avatar: The Last Airbender into a Western fantasy while keeping the plot mostly intact. However, the author hasn't updated for a very long time, so it's sadly a Dead Fic.
NGE: A Century Apart answers the question, "What would happen if Evangelion took place 100 years earlier than it did in canon?"
Matrose Mond by David H. Olivier sets the action of Sailor Moon in Nazi Germany.