Firefox: how can external app get current URL?

In Windows, how can an external app get the currently-displayed URL in
Firefox?

The current-page URL cannot be fetched from any displayed control.  The
displayed URL is not in a "real" control.  This is the case in Mozilla
too, but Mozilla has a handy hidden edit control where this is stashed,
all I have to do is grab the contents of that hidden edit control.
Unfortunately Firefox does not seem to have this hidden edit control so
I need a new solution.

Installing an extension or plugin isn't an option.  Is there perhaps a
message I can sent to the Firefox window that will return its current
URL?

TIA,

-Barry