python-gnome was already installed here, so this worked:
from gnome import gnomevfs
print "%s" % gnomevfs.get_mime_type("/home/user/MyDocs/treeview-tutorial.pdf")

Python also has a standard mimetypes module if an external dependency is not your thing.

(Sorry it's not got CODE tags around it, but my JS is disabled in Tear and the symbol input fails to come up if the clipboard is populated)