what kind of noise do you have? There are a few good audio filters in FCP I don't know about FCE but I think they are there too. Look under: Effects>Audio Filters>
if you are having a low hum, try the Apple AU pass filters and see if you can tone it out with that.
if it is a consistent noise it should be pretty easy with just messing around with the settings.
EDIT: If you can't get it you can email me a clip of the audio uncompressed and Ill tell you how to remove it if you like.