There are only two carriers who operate the Concord, either through BA or AF. AAdvantage members cannot directly redeem awards on BA transatlantic. Since AF is not a partner with AA, AAdvantage members cannot directly redeem awards with AF either.

If you really want to fly the Concord, you can transfer launder AA miles into BA miles through Diners Club. Usually, Diners Club Points convert into BA miles at a 1:1 ratio. The past couple of years, Diners Club has had a promotion which allows conversion of Diners Club points into BA miles at a 1:1 ratio. Its anyones guess if DC is going to have this same promotion this year. I am not sure if you can use DC to launder AA miles into AF miles.

You can also launder your AA miles through HHonors, but the exchange ratio through HHonors is terrible.