Possible Clues:

• Deprived female's lost hat
• Prince's 'Raspberry ___'
• Hat for someone who is very pre-French-ious (a word I just made up)
• Hat worn in France
• Part of the military gear perhaps on top of everything else in France
• 'Raspberry ___' (Prince hit)
• Writer Harte or wrestler Hart
• Brimless, originally Provençal, cap
• Be on time to find hat
• Remember Etonian's hat