Ape Woman, The (1964)
aka's: La Donna Scimmia/Le Mari De La Femme A Barbe/A Most Unusual Woman
A man, Antonio Focaccia (played by Ugo Tognazzi), meets a woman Maria (Annie Girardot), who's body is totally covered with hair. Antonio transforms Maria into a marvel to earn a lot of money as a side show attraction and then later marries her. Very strange and bizarre.
This film is based on a true story, which is featured in the documentary Some Call Them Freaks, also available here at Rare Movie Collector.