A common definition of the term "Renaissance man" is someone who is accomplished in many areas of his life, including the arts, learning, and physical pursuits. Another way to define the term is for someone to be a man of the Renaissance; that is, being a man whose thinking and actions are typical of Renaissance actions and thinking. Using the latter definition, Doctor Faustus is, indeed, a Renaissance man in Doctor Faustus by Christopher Marlowe.
One of the primary differences in thinking between the early Renaissance man and a Medieval man was how he sees religion. While Medieval thinking was God-centered, Renaissance thinking was man-centered. The Renaissance man spent his time pursuing knowledge and exploration of all kinds, particularly scientific exploration, with little regard for God or religion. That is exactly how Doctor Faustus lives his life, in the pursuit of of knowledge, wealth, power, and the mystical arts.
In his first speech, Doctor Faustus outlines the key areas of learning, citing Aristotle (for logic), Galen (for medicine), Justinian (for law), and the Bible (for religion). These were fine for another time (the Medieval period), but he rejects these as worthless notions for his world (Renaissance England). Instead he dismisses God and says he wants to pursue his own desires: magic and the search for things that matter to him, such as riches, knowledge, and power.
What doctrine call you this: Che sera, sera
What will be, shall be? Divinity, adieu.
These metaphysics of magicians
And necromantic books are heavenly;
Lines, circles, letters, characters.
Ay, these are those that Faustus most desires.
O what a world of profit and delight,
Of power, of honour, and omnipotence
Is promised to the studious artisan?
All things that move between the quiet poles
Shall be at my command. Emperors and Kings,
Are but obeyed in their several provinces,
But his dominion that exceeds in this,
Stretcheth as far as doth the mind of man:
A sound magician is a demi-god.
It may seem ironic, then, that the primary conflict of this story is the conflict between God's decrees (of everlasting life and eternal damnation) and man's quest to be god, or at least a god.
Marlowe seems to be warning his audience that taking this new way of thinking (the pursuit of personal glory, knowledge, and riches) apart from spiritual concerns is destined to end badly. Doctor Faustus gladly agrees to sell his soul for these things and he gets them; however, his life degenerates into cruelty and unhappiness. He does have opportunities to make different choices (repent) but does not; Mephistopheles comes for him and Doctor Faustus forfeits his life for things that mean nothing in the end.
As a Renaissance man who represents the thinking of his time (the Renaissance), Doctor Faustus does fit this description.