The fate of Dr. Faustus can be interpreted from both angles. To a large extent, it depends on one's personal beliefs. On the face of it, it does seem that Faustus only has himself to blame for his ultimate fate. After all, he made a pact with Lucifer entirely of his own volition. But on some religious interpretations of the story, most notably that of Calvinism, this is nothing more than an illusion. God has ordained since before the dawn of time that certain people will be damned and others will be saved. There's absolutely nothing that anyone can do to change their fate; it has all been pre-ordained.
The play itself is somewhat ambiguous in this regard. Or rather we should say the two different versions of the play. The Good Angel in the so-called A text appears to suggest that Faustus has the opportunity to repent of his sins:
Faustus, repent yet, God will pity thee. (Act II Scene III)
Yet this is out of step with the overall tone of the A text, which strongly suggests that Faustus' inability to will his own salvation is purely the result of the withholding of divine grace. In the later B text, however, the Good Angel's words are subtly changed to the following:
Never too late, if Faustus can repent.
"Can" implies the possibility, however remote, that Dr. Faustus has the free will necessary to repent.
If Faustus's fate has been pre-ordained by God, then why does the Good Angel appear to suggest that he can repent? Also, why does Mephistophilis constantly seek to tempt and distract him if nothing can ultimately change? Perhaps both the Good Angel and Mephistophilis are simply unaware of God's will. Perhaps, then, there is a gap between their perception of what they think is happening and what's actually happening.
All this is mere speculation. There is no one definitive answer to this question. But there is undoubtedly a qualitative difference between the A and B texts in the treatment of the free will v predestination question. The somewhat ambiguous picture painted by the two texts reflects the mixed theological heritage of the Anglican Church of Marlowe's day, with its Catholic and Calvinist elements.