drag-n-drop is a pretty discussed topic in a lot sites (this too) and i found nice questions too, but no answer to this case.
I have a listView
Think about it for a minute... if you know about drag and drop, then you'll know that the drag source worries about packaging up the data into the correct format and the drag target worries about retrieving the data in the correct format. Your problem is that your drag target is not in your WPF application and so there is very little that you can do as the data is dropped.
A much better solution would be to implement your own basic file browser and then as part of your application, it would be far simpler to access the file path with the drag and drop operation. Either way, you've got a lot of work to do.