I think you may have a problem in writing this paper, because the renaissance started in the 1400s in Florence. In other words, your paper should address how the renaissance impacted Shakespeare rather than how Shakespeare impacted the renaissance. If anything, Shakespeare comes at the tail end of the renaissance.
In light of this, I will give a few points in considering how the renaissance influenced Shakespeare. First, the renaissance allowed people to explore topics that were once taboo in the church. So, we can say that Shakespeare had free reign when it came to topics. He could even portray leaders like Hamlet in very human ways. This would have been unthinkable prior to the renaissance.
Second, the renaissance had an important catch phrase, "ad fontes." This meant, "back to the sources." The spirit behind this was to go back to the classical world. We can see this plays like Julius Caesar, a classical Roman figure. In this way, Shakespeare and others were able to cut through the medieval ages and go back to the classics.