This is a straight forward process IF you do it the right way with the right gear.
Have you loaded the Canon Software?
Then you do not hook the camera up to the computer, you get a card reader, you transfer everything in the DCIM Folder (including that folder) into a new folder on the HD, you put every card into a different folder. So you have YOUR FOLDER/DCIM/100CANON/files .mov and .THM.
In L&T you go to the DCIM folder and everything should be there.
It is a good idea to make your folder a descriptive name since this will be used by FCP as the REEL name.