Marlowe's Faustus begins the play as an ideal Renaissance man. His first scene, as he contemplates the best use of his many talents, illustrates that he is not only familiar with many topics but expert in them. He has fully mastered logic and rhetoric as well as the medieval quadrivium. He has cured whole towns of the disease and seemingly exhausted legal and political studies. After Faust sells his soul in an oddly modern legalistic contract, he gains the power that was also granted humans through Renaissance learning. He embarks on a version of the Grand Tour, where he spoke to learned men throughout Europe. Mephistopheles speaks of circumnavigating the globe, reminiscent of the great explorers of the age. He is also able to secure grapes out of season to satisfy a Duchess's cravings (again, a simulation of what Renaissance trade and navigation would already be able to do). Lastly, his magic allows him to prank the pope and a poor horseman (in simulations of Elizabethan theater's own techniques).

In addition, the prologue tells us that he is something of a "self-made" man in that he comes from common stock, rather than the nobility. Pico della Mirandola's "Oration on the Dignity of Man," perhaps the quintessential Renaissance humanist declaration, also incorporated in Hamlet, celebrates human's ability to choose one's destiny, to sink into bestial oblivion, or though the power of the mind, to rise and exceed even the angels. This concept runs through the play and gives Faust, with his ambitious thought and language, the typical Marlovian anti-hero stamp.

Marlowe, however, is always willing to undercut or ironize the ideals he presents. This is no less true in Faustus. All the while we see a Renaissance man's tragedy, we are also seeing vestiges of medieval morality plays. The good and bad angel who pop up to engage Faustus in a version of the medieval psychomachia (soul-war), the mediation on damnation and journey towards death, and the inevitably comic aspects of Faust's histrionic final scene reflect more a medieval aesthetic.

So, yes, while Faustus is a Renaissance Man who engages in Renaissance ideals, he eventually must pay a Medieval Man's price for his ambition.

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. 

Would you define the title character of Christopher Marlowe's Doctor Faustus as a Renaissance man?

The title character of Christopher Marlowe's play Doctor Faustus has often been called a "Renaissance man," and the designation seems appropriate in number of different ways.  Those ways include the following:

• He is, quite literally, a man living during the historical period commonly thought of as "the Renaissance" (that is, the sixteenth century, at least in England).
• He exemplifes the strong interest in classical literature and culture that was typical of that period.
• At the same time, he shows the influence of Christian ideas, which were also extremely important during that era.
• He exemplifies the greater social mobility common during that period. His parents were "base of stock" (Prologue, 10), but their son nevertheless rose to great social prominence and power.
• He exemplifies the growing importance of formal education and especially university training that was common during this time. He has been to a university and is extremely well educated (which makes his later foolish choices all the more difficult to understand).
• He is interested in, and even expert in, many different areas of learning -- a sense in which we still use the phrase "Renaissance man" today.
• He has the kind of high-flying aspirations that were typical of many people during the Renaissance -- a period (for instance) of enormous geographical exploration.
• He is a "Faustian man" in Oswald Spengler's sense: a man always striving for another achievement, never content with what he already has (although the achievements in this case seem ultimately trivial).
• His chief focus seems to be earthly rather than heavenly, although the main purpose of the play seems to be to check and warn against precisely the kinds of materialistic impulses that motivate Faustus.
• He is an "over-reacher," as was true of many people in the Renaissance. Therefore, almost the final words of the play warn us to

. . . Regard his hellish fall,

Whose fiendful fortune may exhort the wise

Only to wonder at [that is, merely regard with wonder, not actually perform] unlawful things.  (Epilogue, 4-6)