Below, you can see the True North Polar map which shows how the winds actually blow in the northern polar region. By looking at this map, which shows the whole polar region, you can quickly see that there was little chance that Andree could have successfully reached the North Pole, no matter where he started. If the balloon had been more airtight and he hadn't run into ice fogs, he would have simply continued to circle the pole. As it was, he was brought down on an ice floe at about 82° 56' N. lat. and 29° 52' E. long. (Gr.).
What Andree should have done:
Our current understanding of the winds tells us that had Andree wanted to be more successful, he would have left in the winter time. By looking at Winter (January) map, shown below, and following the arrows, we can see that he would have been much more likely to end up in Alaska.
Notice that he still would not have gone over the North Pole, but he would have gone further north, and then probably drifted east until he reached Alaska.