+1 on the concept of exporting your movie from FC as a QT movie along with the sound track. Couple of 'musts' and suggestions...
1) Export using a DV codec, Sorensen 3, or Photo JPEG. All of these decode easily and don't consume a lot of processing power. Were you to export your movie as H.264 or other highly compressed codec, Logic will appear to occasionally choke and generally be less-than-responsive when you play the movie back. The rule of thumb for professional composers using Logic and running QT movies: [b]use DV[/b], period.
You should stream the movie file from a separate hard drive (and never your system drive) for optimum performance.
2) Your QT movie should be overlaid with a time code burn ("window burn") at a frame rate that matches your FC session's frame rate. This is [i]critical[/i].
Fine points: avoid using 00:00:00:00 as the t/c value for the t/c burn at start of your movie, or, for first picture (that's the first frame of film after any leader you may have placed at the head of your film). Otherwise you'll have problems handling the movie in Logic. Best bet? Start first picture at 01:00:00:00. If you have standard 8-second academy leader starting your film (highly recommended you do this), start t/c at 00:59:52:00 right in the leader.
And go one step further: slate the film at the top with a 1-frame-long slate, followed by leader, then the film. If you do this, your t/c burn should start at 00:58:51:XX, right in the slate. The value of "XX" will depend on your frame rate.
There should be no slugs at the start of your film, only leader, "striped" with time code burn.
The time code burn must be contiguous.
Doing all of the above is to facilitate your scoring work in Logic. It's almost impossible to work or communicate (even to yourself) about music placement without a time code burn.