I'm a bit confused; are you asking for information you can't seem to find on google, or are you asking us to do your HW for you ?
Carla Bruni's the French president's wife, and is a former model and is now a song-writer. She's damn hot. She has a child whose father is the son of her ex-husband (Enthoven). Simply look up what a first lady needs to do, I'm pretty sure there is little difference between first ladies in different countries. The fact that she has a child probably means she needs to take care of him/her.
Don't make us do your work for you though D:.