If having the AE clips re-rendered and output in an editing-friendly codec is not an option, use Compressor to transcode all of your h.264 source clips to ProRes. Final Cut will choke on h.264 clips.
The h.264 standard is an MPEG-4 codec designed for delivery, not editing. MPEG-based codecs use interframe compression, which compresses groups of frames together, making it difficult to edit video footage with single-frame accuracy. Video compressed with an intraframe codec needs to first be transcoded to an editable format in order to be edited. HDV is an MPEG-2 based intraframe codec that falls into this category. This is why a very powerful computer is needed to edit HDV, because the clips need to be transcoded behind the scenes in real time into an editable form. H.264 is even worse because it does not have a constant bit rate or GOP (group of pictures) structure, making it impossible to edit.
The “editing” codecs that others have referred to all utilize intraframe compression, in which each frame is compressed separately. This preserves the ability to easily make frame-accurate edits.
By transcoding your h.264 clips to an editing codec, you make it possible for Final Cut Pro to edit them easily. Suggested editing codecs include ProRes, DV, DVCPRO, DVCPRO 50, M-JPEG, DVCPRO HD or 10-bit Uncompressed.