Have a look at this question on stackoverflow:
Upload files to Sharepoint document libraries via FTP
Seems like there is not OOB functionality for this, but ofcourse can be achieved via coding... But I wonder why are you using FTP at all, why not SharePoint Document Libraries to save documents, if the document sizes are the problem then you can use Remote BLOB Storage
EBS (External Blob Storage) in SharePoint 2007
External BLOB Storage (EBS) for SharePoint 2007
If you insist on FTP, then FTPWebRequest is your friend... and you can see how to List Directory details from FTP and Download files from FTP
But you need to make connection to FTP Server each time the user visits the page you are showing documents from FTP on, to overcome that you can either write a TimerJob which timely syncs the FTP with Document Library [overhead, you will be keeping copy of documents at two places] and make the TimerJob to run in off hours, and show the documents from document library!
I wonder, how you are saving permissions in FTP? Please let me know if you need more help!