When AF determines that an FB booking is "suspicious", then the solution is to have the passenger/booker present themselves in person at an AF ticket desk.

It's not so much that the airrport staff can "help"; it's more that airline wants to see the person present themselves in-the-flesh ahead of travel so that a staff member or agent of the airline can verify identities and credit card possession, and determine that there is no funny business.

When the suspicious transaction is due to a broker selling tickets that they had issued using someone else's miles, or where there clearly was an attempt at fraud, the booker/passenger will obviously not want to go to an airport ticket desk. As such, this requirement already weeds out most of the fakes.

However, as with the OP, it will sometimes weed out genuine pax too, if they can't get to an AF ticket desk.