Descartes gives the metaphysical implications of freedom of the will as it relates to the power of cognition. This involves the function of judgement in its natural character and representational function. How does this description deal with infinity and finitude as cognitive? Descartes seems to suggest that the concept of the cognitive is limited by their consideration. So, is the concept of cognition limited or enlarged by the concept of the infinite and finite?
I think this question is best answered with reference to Medieval philosophy. A basic concept in Medieval metaphysics is that effects need a sufficient cause. On Descartes' account of the soul's capacities, we have a limited capacity to know but an unlimited capacity to will. This creates error within us as we can will beyond the bounds of our knowledge. Thus, your question's answer depends on what you mean by cognition.
If you mean the ability to think, then the question is whether this is the ability to think to act or the ability to think to know. On Descartes' account, the latter is limited by the sort of being that we are. We cannot have knowledge in the same way God does. If the former, then this remains unlimited insofar as we control our actions. Both will for Descartes lead to proofs for God's prior necessity for our existence.
If we look at our ability to will, then we need a cause sufficient to enable infinite willing. The proof is by regression. Either the direct cause of a human can give it a free will or it cannot not. If it can give it a free will, it is omnipotent and possesses a free will. If not, then it is insufficient to produce a truly free will. The latter would lead to an infinite series of real things which is considered unacceptable in medieval metaphysics. Ergo, there must be a cause that is infinite, e.g. God.
If we look at our ability to know, then on Descartes' account, we will discover knowledge of the infinite. This knowledge exceeds our imagination (ability to make things up). Ergo, it must have a real external existence sufficient to merit to our knowledge of it. If it were not infinite, it would need to be similar enough to fool us. We must assume we are not so thoroughly deceived (or wind up in the radical skepticism Descartes rejects). Ergo, our knowledge of the infinite proves there is an infinite, e.g. God.
Needless to say, there are several lines of critiques available to reject both approaches: (1) Descartes' arguments only proves we need a cause that exceeds our ability to know (reject equation between this and God, (2) we don't need to reject the possibility of actual infinities (reject medieval assumption), (3) We can believe that we made up the idea of infinity to fulfill our fantasies (reject connection between logic an reality), (4) we can assert that we only prove the existence of a being that asserts our capacities not that such a being is identical with God (reject omnipotence of the cause). These are just a few off the top of my head.