If you are running under a Unix OS, you can use a utility called "lsof" to determine what processes currently have the file open, and the mode used, etc. My lsof binary points to the URL ftp://vic.cc.purdue.edu/pub/tools/unix/lsof, if your system doesn't have it. The exit status of this program is 0 if any programs have the file open.

I really think this is kind of a crappy solution, though, because other programs may have that file open for other reasons that might not be easy to differentiate, and (as mentioned elsewhere), it doesn't help you if the FTP process legitimately closes the file in an incomplete form.