Most FR regions are written to be purposely NOT analogs of historical civilizations, but rather to create an overall high-fantasy feel. Mulhorand, Unther, and Chessenta are the civilizations with the most obviously real-world analogues, followed by Calimshan (although I get the feeling that Calimshan was supposed to resemble a fantasy Koth or Zamora rather than a historical Arabia). Of course, one could attempt to establish closer RW parallels, or (better still!) draw on RW sources to flesh out FR regions. I'd suggest the following:
Cold Lands/Moonsea: 8th-17th century Russia and the Baltic States
The North: A cross between the Canadian frontier/Wild West (the interior) and 9th-12th century Scandinavia (Luskan, Ruathym, etc.)
The Western Heartlands: More Wild West
Amn: Medieval/Renaissance Italy
Tethyr: Medieval France
Calimshan: Medieval North Africa/the Arabian Peninsula
The Dalelands: late-medieval Switzerland or southern Germany
Cormyr: Arthurian England
Thay: early-medieval Byzantium
Mulhorand: ancient Egypt
Unther: ancient Sumer or Babylonia
Chessenta: classical Greece
The Vilhon Reach: Blend elements of Hellenistic Greece/pre-Roman Italy/"dark ages" Italy
Still, I really think that historical analogues are a poor way to go; it seems a much better idea to develop two or three key signifiers for the place (or people from it) and run with that. David Eddings' Belgariad has some nice illustrations of how to do that without getting too fancy (while opinions may be mixed on how good those books are as fantasy literature, IMHO they provide the right level of description and ease of "hooks" for a game).
Incidentally, I think that a number of the "analogues" in the above-linked thread are terrible; how are the Nars more Eastern European than, say, Plains Sioux or Mongol? How are the Lantanna (a race of gadgeteers and seafaring merchants from a subtropical island) like Germans?