On free will, Calvin says:
"Free will does not enable any man to perform good works, unless he is assisted by
grace; indeed, the special grace which the elect alone receive through regeneration."
For him, there is such a thing as free will, but it is not necessarily the same thing as what others mean by the term. This quotation says that our theoretical ability to choose is marred by our total depravity, and only through God's prior, irresistible grace do we gain the ability to choose well. Without that, we "cannot conceive, design or desire any thing but what is wicked, distorted, foul, impure and iniquitous."
At the same time, there is the idea of predestination, which for Calvin is primarily a matter of us being unable to frustrate God's will. The idea of "regeneration" here is that God will "guide, turn and govern our heart by his Spirit", and our free will is thereby reoriented without being destroyed. This doctrine is well-matched by the principle that salvation is not brought about by good works, or any human action for that matter: rather, it is something that God wills for us.
In his Institutes of the Christian Religion, Calvin examined this passage (and the parallel one in Matthew 19:16-22). In summary, he says that Jesus is trying to warn or reprimand the man, by directing him to his sin under the Law:
We also distinctly declare, that if life is sought in works, the commandments are to be observed. And the knowledge of this doctrine is necessary to Christians; for how should they retake themselves to Christ, unless they perceived that they had fallen from the path of life over the precipice of death? [...]
Wherefore, as a teacher of the law, whom our Lord knew to be
puffed up with a vain confidence in works, was here directed by
him to the law, that he might learn he was a sinner exposed to
the fearful sentence of eternal death; so others, who were
already humbled with this knowledge, he elsewhere solaces with
the promise of grace, without making any mention of the law.
(Book III, Chapter 18, Section 9)
and by pointing out his attachment to wealth, which indicates his hypocrisy in assuming himself to be following the Law:
To show him how little progress he had made in that righteousness
which he too boldly answered that he had fulfilled, it was right
to bring before him his besetting sin. Now, while he abounded in
riches, he had his heart set upon them. Therefore, because he did
not feel this secret wound, it is probed by Christ - "Go," says
he, "and sell that thou hast." Had he been as good a keeper of
the law as he supposed, he would not have gone away sorrowful on
hearing these words. For he who loves God with his whole heart,
not only regards everything which wars with his love as dross,
but hates it as destruction (Phil. 3:8). Therefore, when Christ
orders a rich miser to leave all that he has, it is the same as
if he had ordered the ambitious to renounce all his honours, the
voluptuous all his luxuries, the unchaste all the instruments of
his lust. Thus consciences, which are not reached by any general
admonition, are to be recalled to a particular feeling of their
(Book IV, Chapter 13, Section 13)
Jesus is therefore trying to prick the man's conscience: he's not saying that salvation automatically follows from giving up material possessions. In addition, he is speaking to a wider audience (including us right now!), regardless of the status of this particular individual.
Quotations are from the 1845 translation by Henry Beveridge of the 1599 Latin edition of the Institutes, available online here