Please note the Government of France does not recognize the 12-page U.S. emergency passport, issued by U.S. embassies and consulates overseas, as a valid travel document for visa-free entry into France. If traveling on this emergency passport, you may be refused boarding and/or entry by immigration officials. Only direct transit through France for a destination in the United States is permitted with an emergency passport. You should check entry requirements of any other country of destination to make sure the emergency passport is accepted for entry.
According to Section 215 of the U.S. Immigration and Nationality Act (8 U.S.C. 1185), it is illegal for an American citizen to enter or leave the U.S. on anything other than an American passport.
This applies to dual citizens as well, meaning that persons holding e.g. both French and American citizenship and passports must enter and leave the U.S. on a U.S. passport. They may not enter/leave the U.S. on a foreign passport. This applies to children as well as adults.