Jesus on many occasions has used a paradox to explain a truth. To say you can't believe unless God grants it is correct, but not as extremely as you are explaining it. Jesus said in John 15:5 I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
But people "do things" all the time.

Colossians 1:17 And he is before all things, and by him all things consist.

To say everything we do is pre-determined isn't Biblically correct. What is more correct is God knows in advance what we will do, according to foreknowledge. So, the following verse tempers the apparent paradox. Calvin didn't see it going by his teachings.

1 Peter 1:2 Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.

John 12:39 Therefore they could not believe, because that Esaias said again,
40 He hath blinded their eyes, and hardened their heart; that they should not see with their eyes, nor understand with their heart, and be converted, and I should heal them.
41 These things said Esaias, when he saw his glory, and spake of him.

Because of the hardness of their hearts they could not believe. It was a lack of ability because of how stubborn they were, not because God wouldn't allow it. Just like when God said He would harden Pharaoh's heart, he did it with conviction.