The woman in the window is Madame Gertrude Mallory, the owner of the inn across the street. We get a brief history lesson on this lady's life: She's a descendent of a huge hotel family, was educated to become the best, and was left a huge inheritance to set up shop in Lumière. But make no mistake. This lady's made her way through hard work, not her familial connections—the connections just mean that she's got old European traditions running through her veins.
Madame Mallory is described as "a classicist by education and instinct" (4.5), and her favorite possession is a cookbook dating back to ancient Rome. Yep, this lady goes by the oldest book on the European shelf. So in other words, she's basically the antithesis of her new neighbors.
The day that the Haji family arrives is Mallory's birthday. Her cooks surprise her with a cake and sing "Happy Birthday" to her… and she responds by throwing a tantrum and stomping off, saying that they're ridiculous and wasting their time.
In her bedroom, she looks in the mirror and realizes that she's not going to get younger or more famous; suddenly, she feels like her life is worthless. Why at this moment? We're not totally sure, but birthdays can do that to a person.
The next day Le Saule Pleureur is closed for lunch. She looks out the window and sees the Haji's topsy-turvy world being unpacked from the caravan.