Scripture has its authority from God not the church.
But a most pernicious error widely prevails that Scripture has only so much weight as is conceded to it by the consent of the church. As if the eternal and inviolable truth of God depended upon the decision of men! (1:75)
The apostles had authority prior to the church because the apostles and prophets were the foundation of the church [see Ephesians 2:20] (1:75)
In order to accept Scripture as Scripture we need the witness of the Holy Spirit. Calvin does acknowledge that there are rational proofs that God speaks in Scripture – proofs that should be accepted by all but the most hardened. Yet, he clearly states that without the work of the Holy Spirit, no proof will be enough to convince them.
The testimony of the Spirit is more excellent than all reason. For as God alone is a fit witness of himself in his Word, so also the Word will not find acceptance in men’s hearts before it is sealed by the inward testimony of the Spirit. The same Spirit, therefore, who has spoken through the mouths of the prophets must penetrate into our hearts to persuade us that they faithfully proclaimed what had been divinely commanded. (1:79)
Calvin concludes that Scripture is “self-authenticated” by the Holy Spirit and not by proof and reasoning.
And the certainty it deserves with us, it attains by the testimony of the Spirit. (1:80)
Bonus word regarding “new revelation”. This is not set in a context of modern claims that God still gives prophecy, but it seems to apply.
Now daily oracles are to sent from heaven, for it pleased the Lord to hallow his truth to everlasting remembrance in the Scriptures alone [cf. John 5:39] (1:74)