Click on the Insert menu then on the Quick Parts icon. Pick Field from the drop down list. In the categories drop down list pick Document Information and in the Field Names click FileName. Decide which format you want (I always use lower case to distinguish a file name from a folder name for which I always use UPPER CASE) then click the Add Path to Filename box. Click OK and you're done.

It doesn't have to be a footer this can go anywhere on the page. The file is saved with the full path and file name and you don't have to mess around copying to the clipboard and pasting into whatever file you are sending.