OK I can't seem to locate my source for the second offer that came in 1700 but I do have multiple sources from the 1697 one; William had no intentions of forcing the Prince to be raised Anglican but was content to allow him to continue to be educated in the Catholic faith. The issue with the 1697 offer was that William wanted custody of the Prince of Wales, something the King and Queen refused to entertain; apparently there were fears that he would poison him but I don't give much credence to that fear. I remember that the second offer had dropped that requirement.
@jb3, not true. William never PUBLICLY acknowledged the Prince of Wales but privately had no doubt that he was his first cousin. According to Lord Ailesbury, He asked to see a portrait of him, and remarked, "About the mouth he is most like my uncle King Charles, and his eyes are most like to his mother's." Plus William acknowledged the legitimacy of the Prince in conversations with Electress Sophia, even though it was in both of their interests to do otherwise. The Only one that stubbornly clung to that theory was Anne herself.
And I actually had a good scenario for this situation; in 1700 Anne had her last pregnancy, a stillborn child. So my idea was this kills her, then in July Gloucester dies on schedule. The second offer is made (that let James stay with his parents) and Louis XIV forces his cousin to accept it. The Act of Settlement isn't passed and instead the King, with the Tories, pass a one-off bill to allow the Prince to succeed as a Catholic. Come James's death in 1701 the Jacobites and France do nothing, meaning that the Spanish succession war is averted (or at least severely curtailed) as the proclamation of James III & VIII is what drove Parliament to support William's rearmament and opposition to the succession of Felipe V in Madrid. Now who would be the Regent or whether Parliament would chose to use the Richard II precedent I don't know, but effectively Louis XIV would have given two Kings to two countries and created a situation in which three Kings (or potential Kings; Bourgogne, Anjou and Wales) were close childhood friends, raised in close proximity to each other. That would be entirely unprecedented in modern history and could mean a League of Spain, Britain and France emerges later on.