Here is a long post I put in the coronavirus forum, moderators feel free to delete it as it is a duplicate and we did not fly AF this time (AA in business was just too cheap to not do it), but I think it will help some readers of this thread:
o here is our experience yesterday, traveling AA LGA-DFW-CDG. One dual US and French citizen, and one US spouse.
At LGA the AA check-in staff was nice but it took them 45 minutes to get clearance for the US spouse, they had to make phone calls to verify it was allowed and to unblock the reservation. They did check our US marriage certificate. They did their best and had a positive attitude. Then no question asked until CDG, we needed three forms each to board the transatlantic flight: reason for travel declaration, health declaration and tracing form.
Arriving in CDG the immigration agent let us in after checking our “livret de famille”, which shows the acknowledgement of our US marriage by the French authorities. The US marriage certificate may have been enough but I did not show it. The three forms we each had to fill and sign were never requested and are still in my bag....
Note we also had a plan to continue onto Austria and scraped it. We had recent virus test certificates so technically I think they would have let us in but the friends we wanted to visit in Vienna were very uncomfortable. They had talked to people around them and everyone told them that their neighbors might complain, that the authorities may force us into quarantine anyway, that they would have to quarantine themselves after our departure, that even with a recent test there was too big a risk we could get contaminated inflight... Given that we did not want them to feel uncomfortable for all that time we just skipped the trip. Interesting case of peer pressure.
Also of note, the first hotel we stayed at in France almost canceled our booking when they saw a US address, and finally after we mentioned having tested they put us in a nice room in a separate building. Not ideal but I understand their concern. We are taking a calculated risk but not everyone has to play along with us.