Madame Bergeret is hoding her "Bergere" straw hat, also known as the "Shepherdess," "Milkmaid", or "Skimmer." They were often worn "gipsy" style, with a ribbon that tied under the chin encircling the head. Bergeres had long been worn in rural England; in August 1667 Samuel Pepys noted in his diary that the ladies in the country wore these straw hats, which "...did become them mightily." Straw had been used in hatmaking for centuries, the finest was Leghorn or Tuscan straw from Italy. The scarcity and expense of this straw caused local milliners to experiment with different native straws. Soon English and American women were making fine straw hats. It was a laborious process; the straw was first split, then plaited (braided) into sections which were then sewn together by hand, and blocked into shape.
from HATS & BONNETS by Susan Langley, Collector Books, 1998.
Womens straw hats, similar to the one pictured here can be seen at The Village Hat Shop.