Yes, we tend to think of Claude as a male name and Claudia and Claudette as the female, but this ancient clan name is used in France for girls as well as boys, and could make a distinctively chic choice here too. You may be surprised to know that Claude was in fairly regular use for American girls in the 1880's and nineties, reaching as high as 553 in 1880.
In her native country, there have been some famous female Claudes, including Queen Claude of France (1499 to 1524), daughter of Louis XII, and another sixteenth century Claude de France, daughter of Henri II.
Later Claudes include the daughter of Claude Debussy, Claude-Emma (called Chouchou), the leading female character in Tracy Chevalier's novel Lady and the Unicorn, French actress Claude Jade and photographer Claude Cahun, and the widow of French Prime Minister Georges Pompidou.
While the "lame" meaning is the most widely acknowledged, some etymologists theorize that the name may relate to the word for enclosure or clause, an alternate meaning that may appeal to a child with a form of this otherwise-appealing name.