But did the French not have an option to reclaim New France, in return for handing over some Carribean island? I seem to recall that from school with the French government deciding that the island was more profitible.
No. You are thinking of 1763, after the Seven Years War, not 1783. In that case, the British had the option of choosing (or rather had a debate on which of these they should demand to keep) either New France or Guadeloupe. They chose New France.