OK, I just tracked down a Boucheporn portrait to complete our portrait analysis of Napoleon III paternity candidates. Here is René Bertrand de Boucheporn's brother, Anne François Louis Bertrand de Boucheporn:
Interestingly, René Bertrand de Boucheporn named his daughter Hortense. Hortense married into the de Sampigny family, and one of her descendants, her namesake Hortense de Sampigny, became a famous violinist (she's on the left, of course):
Intriguingly, the Bertrand de Boucheporn family is thought to have originated in or near Metz, which is a relatively high I2-M223 area. That said, I'm not sure I see a lot of family similarity to Napoleon III with them. Does anyone?