I'm not sure when you consider a man "regenerated", I have to guess you talking about being born again as a new creature? If so this is certainly something that happens upon condition of faith. Moreover always happens given those conditions according to John 3:16.
But then, deciding to have faith in God seems like a decision of the individual to me. Indeed, the central most important decision of our entire existence.
It seems odd that such a decision could be made without any desire at all to draw near to God.
Thus, for consistency, I can see why the Calvinists must reject the concept of free will in the matter. I will grant that these doctrines give mutual support, but I can't see much motivation for either outside of a perceived contradiction between God knowing what man will decide ahead of time, and yet still allowing man to choose.
Reading C.S. Lewis has cured me of supposing there is such a contradiction.
***It seems odd that such a decision could be made without any desire at all to draw near to God. ***
You are ABSOLUTELY right in this. Unregenerated man CANNOT draw near to God. He has no DESIRE to draw near to God. He is DEAD in his sins, a slave to sin, and has no ability to draw near to God. God puts the desire, the faith, in man to draw him to God. It is all the works of God, so that no man can boast. It is the FREE gift of grace, not a grace that man can earn.
As I have said before, this is how “free will” works:
Unregenerated man has the “free will” to choose to sin or not sin at any given time.
Regenerated man has the “free will” to sin, not sin, or please God.
We all make choices every day. However, the unregenerated man will NEVER choose to please God, because he can’t.