This little item casts a lot of doubt on the identification of the head as Henri IV:
http://omicsonline.org/open-access/discussion-surrounding-the-ident...
They do make a not entirely warranted assumption late in the paper, that Louis XIV and his brother Philippe had the same father (confirmed by the Bourbon Y-DNA analysis, since two of the samples were from descendants of Louis and one from a descendant of Philippe), and that said father was Louis XIII (presumptive but hardly conclusive).
There are no other male-line descendants of Louis XIII, or his (probable) father Henri IV, available for testing, so the matter rests there.