We receive salvation by His grace through the free gift of faith in Jesus Christ, from God alone. That's what the words say. Just like the words of Paul.
We don't "bring our faith" in order to believe. We bring our faith to every moment in our lives because we believe according to God's gift of grace.
On the surface, it's semantics.
In truth, it is the very reason for the Reformation -- it divides those who believe in salvation by the grace of God alone from those who believe in salvation by men's good and inbred righteousness, ability, works, tithing, piety, connections, professions, intelligence, luck.
But none are righteous. We are all fallen and dead in sin, unable to rebirth ourselves. "Nothing connected with it is our own." Like Lazarus' second life, only God can breathe righteousness back into the dead corpse of the fallen sinner.
There is not an Arminian on the threads (that I know of) who would disagree with Calvin's statement.
The fact is, faith comes before regeneration, not after, since there is something man has to do before he is born again, he has to believe