PsFile does work on remote machines. If my login account already has access to the remote share, I can just enter:
psfile \\remote-share
(replace "remote-share" with the name of your file server) and it will list every opened document on that share, along with who has it open, and the file ID if I want to force the file closed. For me, this is a really long list, but it can be narrowed down by entering part of a path:
psfile \\remote-share I:\\Human_Resources
This is kind of tricky, since in my case this remote share is mounted as Z: on my local machine, but psfile identifies paths as they are defined on the remote file server, which in my case is I: (yours will be different). I just had to comb through the results of my first psfile run to see some of the paths it returned and then run it again with a partial path to narrow down the results.
Optionally, PsFile will let you specify credentials for the remote share if you need to supply them for access.
Lastly, a little known tip: if someone clicks on a file in Windows Explorer and cuts or copies the file with the intent to paste it somewhere else, that act also places a lock on the file.