Zope has a built in [Zope and WebDAV] server (this needs to be enabled in INSTANCE_HOME/etc/zope.conf), which can be used to mount a ZODB as a virtual filesystem.
Zope and WebDAV clients reportedly working well for this are the built-in client in Mac OS X and davfs2 on Linux (see for example How to access the ZODB as a filesystem). The Windows built in DAV support ("Windows Web Folders") is often stated as being buggy and not really working with Zope Zope and WebDAV, but lately from the side of Zope this appears to have been fixed somehow, see https://bugs.launchpad.net/zope2/+bug/143447