That’s strange. How did you install it?
If you installed it manually you might have come across a problem whereby the .zip archive of Facebook Events made available at Account Central > Downloads is “double-wrapped”, so if for instance you unzipped it locally you might have ended up with a directory called:
the-events-calendar-facebook-importer.1.0.3
However the plugin directory itself would be inside this and would actually be named:
the-events-calendar-facebook-importer
(If this is the case you may find another sub-directory called __MACOSX in there too.)
Are you able to look inside your wp-content/plugins directory using FTP software (or your hosting control panel) to check out if this is indeed the problem?