My family is composed of US and French citizens, and lives in the US. My wife, myself and two of our children are French citizen, with an I-765 EAD/AP ("Combo Card") and an H1/H4 visa. We all have French passports. Our third child is an American and French citizen (dual citizenship), she is an infant, has a US passport and is in our "livret de famille". She does not have a French passport nor a "carte d'identité".
We are going to travel from the US to France and back soon, and wonder what we should do at the border. As far as I know, the border (both in France and in the US) at the airport is always divided in a "Citizen" / "Visitors" way, like this:
Since we are all French citizen, I would assume that she can cross the border with us (i.e., come with us to the "E.U. Citizen" kiosk), and that our "livret de famille" will be enough to prove her citizenship.
Am I right in this assumption?
Or should she go with one of us trough the "visitor" kiosk? Worst case scenario, US citizen do not need Visa for short visits in France, if they have a US passport, according to france-visas.gouv.fr, so she should be able to enter France easily.
Entering the US
I don't know if we should go through the "US citizen" or "Non-US citizen" kiosk to re-enter the US. Since she is a US citizen, she should go through that kiosk, but none of us can go with her, and she is obviously too young to go through custom on her own. Since she does not have a I-765 EAD/AP ("Combo Card") or H4 visa, I feel like it would be inappropriate to try to go through the non-us citizen kiosk with her.
I asked a travel agency and looked around, but could not find the answer to my question. Should we all go to the non-US citizen visitors?