"Free will" / "will" does not appear in Jn 6:44, or Jn 6:65. It is thus easy to draw wrong conclusions about the role of the human will from these passages.
This is your first fallacy: to make out that God's enabling overrides the will of man, but consider the converse. In the biblical record of Pharaoh's hardening his heart against God & Moses, sometimes it is said that God does it, sometimes it is said that Pharaoh does it. So in that case, God's "enabling" never supervened Pharaoh exercising "his" own will, which wasn't "free" in biblical terms as constrained by sin, yet it was still "his" own will, as scripture itself concedes.
So, God's grace doesn't vitiate human will, albeit human will cannot escape God's purposes in its decisions.
As to "free will", the Calvinist confounds the terminology. There is human will, and there is "free will," which has no true biblical application except to the saved, per John 8:36. However, even those with a measure of "free will" may forfeit both grace and grace's freedom by apostasy. One who rejects the gospel is either rejecting God's drawing (or calling Matt 22:14), or is already past the point of no return, as Pharaoh was, as affirmed by Stephen in Acts 7:51 of the very Jews to whom Christ spoke.
This leads on to the fallacy of "irresistable" grace versus the human will. Per Acts 7:51, anyone who denies that grace can be resisted is repudiating what is self-evident.
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