Albeit somewhat tangentially, I've covers this topic in two posts one on Eleanor as heiress and another more theoretical assessment of her supposed adultery and its contemporary treatment.

Ultimately, I think Louis was in love with Eleanor, a young bride chosen for him by his savvier father, but ultimately unable to carry on the relationship that not even the pope could save. By the time he realised the full extent of his error it was far too late and perhaps one of the most profound errors made by a medieval French king.

This is a tricky one simply because we still don't know whom actually initiated the divorce proceedings-it is a debated topic. Assuming Louis desired the divorce more (due to Eleanor's behaviour on the crusade-including a likely liaison with her uncle, Raymond of Antioch and general infidelity) then perhaps he did not think that Eleanor would marry so quickly. It should also be noted his advisors such as Abbe Suger advised against the divorce because of the land/money Eleanor brought to the union. However Louis was excessively pious and so with Eleanor's unchaste behaviour he may have assumed that no one else would desire such a wife irrespective of her wealth and land. Also Louis would have been unlikely to suspect that Henry (II) would be a viable candidate due to the known relationship between Eleanor and Henry's father, Geoffrey of Anjou, again to to his overly pious nature as such a union would be incestuous to Louis. Louis did not try and choose Eleanor's next husband irrespective of who initiated the divorce it is accepted that Eleanor had little regard for Louis, and that he was saddened by it. He also had little opportunity-Eleanor remarried in two months.