Possible Clues:

• By the sound of it, fruit goes on ahead
• Canvas filler's cap
• Frenchman's topper
• Groucho wore one
• Topper with a tab
• Soft, brimless cap
• Parisian's head cover, maybe
• Round, brimless cap
• Soft round cap without a peak
• As a Basque, it may go to one's head