Searching FTP with the search facility of this site, I found http://processing.org/hacks/doku.php?id=hacks:ftp which shows how to use a library to do FTP stuff. There is a section showing how to get a list of files.

Writing to it: download, append, upload.

If you can get a directory listing, you can loop through it and check for the file of interest, and that link that PhiLho posted shows how to get the listing, so see if you can figure out how to edit that sample code to get what you want.  You'll want to use string.equals to test for string equality rather than == (see http://processing.org/reference/String.html and the links there).  If you have trouble, feel free to ask for help, but it's always better to try to figure it out first - the example code there is pretty clear, so I think you'll get a lot more out of playing with it than if one of us posts a cut and paste snippet.