The work traditionally seen as the core of the Old French Crusade Cycle, La Chanson d’Antioche, is an account of the First Crusade which did not, as far as it is possible to tell from the surviving cycle manuscripts, take up any elements of the history of the early Latin Kingdom of Jerusalem. Other parts of the cycle, either composed separately and grafted onto the Antioche or composed by the cycle remanieurs to continue the story are, however, set in the historical world outremer.
For bibliography and further info on the crusade cycle see
Arlima