How do you think Pope Francis reconciles his belief in the bible and his statement of the truthfulness of the Big Bang Theory and Evolution?

Nothing to reconcile. The only people who assert there is a conflict are atheists and YEC's. Both based on an errant and unscholarly interpretation of Genesis that did not even exist until the 17th century.

The same way most Christians do - by recognizing the truth. Evolution is true. And, not all of the Bible is literally true, eve though it is all good for us.

Easily. Catholics do not take the creation stories as 'fact' but as fables and parables, as they are meant to be taken.