Here is an answer in two parts. The first part deals with information extracted from Book 1 of Calvin’s ‘Institutes’. The link given opens up at Book 3 so you have to navigate back to Book 1. https://reformed.org/master/index.html?mainframe=/books/institutes/books/indxbk3.html
CALVIN INSTITUTES - BOOK I. THE KNOWLEDGE OF GOD THE CREATOR. Discussion of Human Nature as Created, of the Faculties of the Soul, of the Image of God, of Free Will, and of the Original Integrity of Man's Nature: Section 15: STATE IN WHICH MAN WAS CREATED. THE FACULTIES OF THE SOUL - THE IMAGE OF GOD - FREE WILL - ORIGINAL RIGHTEOUSNESS.
Manichaean error of the soul's emanation: It must, therefore, be held as certain, that souls, notwithstanding of their having the divine image engraven on them, are created just as angels are. Creation, however, is not a transfusion of essence, but a commencement of it out of nothing. Nor, though the spirit is given by God, and when it quits the flesh again returns to him (cf. Eccl 12:7), does it follow that it is a portion withdrawn from his essence.
Opinions of the philosophers on the soul criticized in view of the fall of Adam - The soul and its faculties: It were vain to seek a definition of the soul from philosophers, not one of whom, with the exception of Plato, distinctly maintained its immortality. Others of the school of Socrates, indeed, lean the same way, but still without teaching distinctly a doctrine of which they were not fully persuaded. Plato, however, advanced still further, and regarded the soul as an image of God. Others so attach its powers and faculties to the present life that they leave nothing external to the body.
Free choice and Adam's responsibility: At present it is necessary only to remember, that man, at his first creation, was very different from all his posterity; who, deriving their origin from him after he was corrupted, received a hereditary taint.
NOTE: Immortality of the soul does not mean the soul existed from eternity. Immortal means it does not die, not that it always existed.
Nowhere does Calvin suggest that human souls pre-existed. On the contrary, he declares that souls are created and have their commencement “out of nothing”. Souls are created in time, not before God created time, space, matter and all life as we know it.
The second part to this answer has more to do with Calvin’s view of the soul separating from the body at death and how Scripture shows that the soul is immortal, that it continues to exist after death. Source: http://archive.churchsociety.org/churchman/documents/Cman_105_3_Hallett.pdf
When, in Inst. 1:15:2, Calvin talks of the soul being the ‘nobler part’, he does so arguing from Scriptures which clearly distinguish the soul from the body and emphasize the immortality of the soul. It is in this sense that Calvin then concludes that the soul is the ‘principal part’...
When we consider for example, that in Institutes 1:15:2 Calvin refers to no less than sixteen passages in Scripture which talk of the soul and body separating at death, and that he only uses the word ‘flesh’ when the New Testament uses it, then it is harder to accept that Calvin is Platonic in this area, rather than Biblical. [p 5]
It is perhaps impossible to ascertain exactly the Platonist influence on Calvin. He was certainly well versed in both Plato and Plotinus and, of course, in Augustine and this may well have resulted in certain tensions in his thinking, reflected, perhaps, in the Platonist language and terminology he frequently used. But, having said that, it appears that his overriding concern was to allow his theology to be shaped by Scripture. [p 6]
The soul, then, is something essential apart from the body and is, argues Calvin from Scripture, ‘the principal part.’ It is the soul which survives when freed from the prison house of the body and it is the soul which bears the image of God. Calvin puts it this way: ‘For although God’s glory shines forth in the outer man, yet there is no doubt that the proper seat of his image is in the soul.’ [p 7]
It is worth repeating that the biblical doctrine of the immortality of the soul does not mean the soul existed from eternity. Immortal means it does not die, not that it always existed. There is no attribution of ‘deity’ to the human soul, even though the first man and the first woman were created “in the image of God.” Neither does Calvin suggest that human souls pre-existed in some heavenly or spiritual realm and were then “transferred” into human bodies at some later point in time.
(NOTE: Emphasis in quotations added by me)