It will all be down to time.
BA have normally 5 or 6 aircraft serviceable at any one time and require 4 aircraft to run a twice a day return to JFK and 5 to also run the weekend barbadoes winter service. leaving 1 for charters and 1 under a C check.
Their priority is the JFK route, but it may not support a 2 flights a day return service until passenger confidence re-builds, but I suspect they could still fill the bird on a flight to barbadoes.
who knows what AF want to do, if they decide not to continue flights BA would jump at the chance of aquiring the 5 remaining aircraft for thier use as they have, on average, only 60% of the flight hrs/cycles of the BA fleet.
For more info see the Concorde website http://www.concordesst.com