1)  You have two files on the destination folder. One with the original name and one with an extra ".PART" extension. Move the .part file to some other folder (Move! not copy), and delete the file that has the original name.

2)  Start your download again from the beginning.

3)  Let it download a few bytes, just to have those two files created again, with the exact same name. Now PAUSE this download.

4)  Go to the folder where you backed up the old .part file.   Move it to your download folder to replace the newly-created .part  file.

5)  Now go to Firefox's Downloads form and resume the download.   Instead of picking up where it just left off, it will pick up from where the (newly-moved) .part file left off.