Bringing Up Bébé is a book memoir combined with a book on parenting advice. The main point is that the culture of parenting in Paris is different than in America. She does a good job of distilling the differences down to something digestable and beyond anecdote from her personal experience. There are reasons for why the cultures have developed certain attitudes towards child rearing and these differences have an impact on the lives of both parents and children. Most of it is driving a narrative that the French system is better, but there are some tempering points about why things are not always "better".
It is not worth going through the book point by point, but there are a few high level themes that I took away. The main one being that children are complex humans with rich inner lives. The American way of viewing children tends to see them as not being too simple to have serious emotions and viewpoints and that they need to be constantly coddled. Parents think they need to be constantly entertaining and micromanaging children. The French view of children is that they need to be given space and respect for their own inner selves to exist and interact with the world. This leads to things like let children eat real food, make them eat in the same schedule as the rest of the family, let children spend time alone, give children wide freedom while they are inside a well structured frame (cadre) but be strict at the boundaries.
The other big point which I think might be difficult for me is to be strict. A parent must be the one who ultimately decides and is the one who is firmly in charge. It sounds clear in theory, but I can see how this would be difficult.
Overall I enjoyed this book, and I am sure I will go back to it and check some things out when I am not sure why nothing seems to be working.