The US Embassy in Paris replied with the following guidance:

“Adults traveling in or out of the United States with children under the age of 18 should be aware that Customs and Border Protection (CBP) strongly recommends that unless the child is accompanied by both parents:

• the adult have a note from the child’s other parent (or, in the case of a child traveling with grandparents, uncles or aunts, sisters or brothers, or friends, a note signed by both parents) stating “I acknowledge that my wife/husband/etc. is traveling out of the country with my son/daughter. He/She/They has my permission to do so.” CBP also suggests that this note be notarized.

We recommend all minor children and adults have a copy of their passports available in case of loss or theft, and copies of their birth certificates.”