If you wish to consider a partial or full day (two nights) in Bordeaux, before you strike out for Bergerac, there are interesting sites there, including the Musee d’Acquitane, Musee du Vin et Negoce, Cite du Vin and lovely city gates. At the Musee du Vin et Negoce, we learned quite a bit about France’s and wine’s role in the “circle trade,” i.e., the slave trade.
We also enjoyed a brief wine tasting “class”
In the city, learning about all those descriptions of tastes and getting a bit more of an appreciation of mineral, melon, pineapple, apple, cherry, plum, licorice and tobacco as descriptors, as well as learning about the five distinct regions or terroirs that we lump together as Bordeaux.. Don’t know how a class like that would work for your 13 year old, though.
Rick Steves France Guidebook (and website) entirely ignores Bordeaux. Lonely Planet has a pocket guidebook to Bordeaux that we found useful. (Perhaps the fact that RS ignores Bordeaux is also useful.)
BTW, your daughter might enjoy learning a bit about Ailenor of Aquitaine, one of the most remarkable women of the Millenium. She was raised in the medieval court of Aquitaine (in Poitiers), daughter of the Duke, literate, musical, became Duchess (and ruler) of Aquitaine, and later married Louis VII. She went on a Crusade with him where she outshone him as a military leader. After they returned to France, she got the Pope to anull their marriage, so she could marry Henry II of England. Her children included Richard the Lionhearted and King John. She is buried in the Loire Valley (sorta between Chinon and Saumur) at Fontvraud Abbey, alongside Henry II and Richard Coeur de Lion.
A final comment, while Bergerac has a pretty, touristy district, I was not particularly captivated by that town. The Dordogne region east of there was, as the French say, formidable! (Tremendous). Consider including a visit to Chateau des Milandes, home to a remarkable woman of the 20th Century, Josephine Baker along your journey.
Bonnes Vacances.