FCP doesn't work with H.264 files....nor MP4. If you don't see the codec listed in the EASY SETUP list...don't use it.
Are the large files ALSO H.264...say from a Canon DSLR?
You need to convert the footage to codecs FCP works with, like ProRes. And ProRes files are LARGER than camera raw H.264...but are easier to work with.
If you want to edit natively, or with H.264 files...you need to be using Adobe Premiere Pro...or FCX.