Call most convenient one first (prob US) and if that doesn’t work call again (US line or otherwise AF international). I’ve had very good support from AF during changes to both paid and award tickets where the departure time was changed. I don’t know all the minutiae of the fare rules, the service desk agent often sees schedule changes as a hinderance to the customer and often tries to resolve it within their technical capabilities. Why I said try again is because the willingness to help out is not always dependent on rules but also the agents knowledge on the rules, their ability to make the changes and downright character/service mentality (or crankiness that day). What agent 1 told to me would need to go to backoffice, agent 2 made happen with 2 clicks when I called back later in the day.

finally: should you run into multiple no’s where you ask them to help out based on their schedule change: then (and only then), swap to the question where you are entitled 1 free stopover on an award ticket. This is not an ideal route because sometimes they charge for it if they process it as a change/rebooking; and it depends on the award rules at the time of the change: meaning the departure and final destination could in the meantime have increased the miles required (which is not good for you) and it depends on whether each leg incl the new first leg has award availability. If the preferred earlier flight simply has no award availability then you might not be able to claim the free stopover option. FB service desk can figure all these things out for you, but never give up upon 1 no.