From Civfanatics FAQ:
How can I get the game to run in a higher resolution?
By default, the game runs in a 1024x768 resolution. To get it to run in a higher resolution, navigate to your Civilization 3 folder (default: C:/Program Files/Infogrames Interactive/Civilization 3/ -- if you have PTW or C3C, go to that folder inside your Civ3 one), and open your .ini file (named Civilization3.ini for Vanilla, ptw.ini for Play the World, and conquests.ini for Conquests). Add a line at the bottom that says: KeepRes=1 . Now, when you load your game, it'll use your computer's default resolution.
Look for one of these ini files.