Like
adicoto mentioned you can find it in ffdshow!
With an appropriate moviefile loaded:
(rightclick >) Options > Filters > Advanced.
Click on the small [+]-sign of "ffdshow Video decoder"
Then click on "ffdshow" followed by
selection of "Codecs" in the colum in the middle (with a slidebar).
Then in the window most right (with a slidebar) there is the "Format"
(default at the fouth place from the top) "Other MPEG4".
If you check the list you will see it also includes FMP4.
(You can rightclick on the line to (re)assign the format to a different decoder/filter
and/or you can click on the decoder mentioned and change or disable it for the selected format.)
You can add the extension to BS.Player yourself under
(rightclick >) Options > Preferences > General > File types
Just to the right of the list of "Associated extensions" type "FMP4" in the blank box above the button (
Add extension) and ... (etc.)