Travel with small dog, US to France

Question
Hi, I like to know what is requirement travel with dog US to France and coming back.  I understand there is not quarantine from Us to France, how about coming back? Any problem? besides health certificate, necessary shots and microchip...what else? Do I need to get approval from USDA?

Answer
To enter France:  Microchip.  Rabies vac at least 30 days old and
less than 1 yr.  APHIS 7001 international health cert issued within
10 days of travel and endorsed by usda.  Most important: EU form 998
English-French and endorsed by usda.  This cert can be up to 4 mos
old.
To re-enter USA. Very easy, No quarantine.  Health cert issued within
10 days of travel and a valid rabies vac.
Best to take dog as excess baggage.  Much cheaper and would clear
customs with you
Regards, Jerry Mishler