Your question isn't exactly clear. You are employing an English language idiom "pay the price" that does not have a literal meaning in this usage. What the idiom means is that you suffer the negative consequences or results of something wrong or risky that you or someone has done:

• McGraw-Hill Idiom Dictionary: to suffer the consequences for doing something or risking something

In light of this idiom definition, your question is really asking, in paraphrase:

• Is Doctor Faustus a Renaissance Man who had to suffer unpleasant consequences for his actions that were more appropriate for a Medieval Man to have suffered?

Answering this requires understanding three things: (1) the primary relevant characteristic of a Renaissance Man; (2) what wrong or risky thing Faustus did that he'd have to "pay the price" for; (3) the contrasting primary and relevant characteristic of a Medieval Man.

(1) Faustus exemplified the Renaissance celebration of the expansion of knowledge. The rediscovery of ancient Greek and Latin texts opened new fields of study and new ideas for Europeans and excited the minds of the intellectuals leading to a blossoming of intellectual and scientific thought (this later was labeled the Renaissance). This exploration of knowledge put a new light on individual accomplishment and individual identity because intellectuals could see what others had done before them and what being in the shadow of a religion-dominated intellectualism had left unexplored.

(2) Taking the Renaissance spirit of exploration and individual freedom and power to the extreme, Faustus wanted unlimited knowledge (knowledge of God and his ways) and unlimited power (for wealth and control of the natural elements).

FAUSTUS. O, what a world of profit and delight,
     Of power, of honour, of omnipotence,
     ...
     All things that move between the quiet poles
     Shall be at my command:
     ...
     A sound magician is a mighty god:

(3) Contrastingly, Medieval Man was focused on the doctrine of the Christian Catholic Church and was governed by the presence, if not the law (though sometimes both), of the Church. Best known among the great Medieval thinkers were Charlemagne and Thomas Aquinas. Charlemagne was integral is establishing the Holy Roman Empire and Aquinas was integral in detailing Church doctrinal interpretations. Because religion so permeated Medieval life and thought (think of the religious themes and satire in The Canterbury Tales), good and evil, damnation and salvation, forgiveness and punishment were dualistic ideas that held dominance over even common people, like those peasants who bought Indulgences from pardoners. 

Now to your question: Faustus pursued the Renaissance ideals in knowledge and individualism. In this way he is the ideal Renaissance Man. Yet, he pursued these to their extreme limits: he sold his soul to Lucifer via Mephistopheles. In this way he was thrust into and re-enlivened the narrow emphases of Medieval thought. This may be seen as a Renaissance Man suffering the consequences of a Medieval Man's thought system: he was thrust into the living dualities of good and evil, damnation and salvation, forgiveness and punishment and was subjected to the domination of Lucifer (ironic because Faustus sought complete domination of the universe). In this sense, the answer is "Yes," though it is also "No" because the principles of Christianity had not died in the Renaissance, they had only been reduced in intensity.