AUC is high but not able to represent other class properly
It does not make sense to make two separate AUC / AUROC curves for each class, these are aggregating functions, same as F1-score. If AUC is high but F-score is not then it's possible you have an imbalanced data set (classes are not equally represented in the data), since the AUC will not be able to measure this, while the F-score does. So, if you do have an imbalanced data set you should use something other then AU(RO)C, such as the F-score.