I’ve often been told by Arminian heretics that Catholics entertain some form of Calvinism. Nothing could be more grossly misrepresented in the whole of Catholic theology than this idea that the Arminians maintain. I imagine they do this in order to defend their own beloved heresy of total depravity. The problem is that any meaningful dialogue between the Arminian and the Catholic will enable the Arminian to realize that while the Catholic holds the Arminian view of soteriology to be heretical, the Catholic also explicitly denounces the Calvinist heresy for similar reasons.
Exactly, where is it gathered that Catholics are Calvinists any way? My Wesleyan Nazarene friends lay the blame all on St. Augustine. But the problem is that Wesley did in fact draw upon the theology of St. Augustine to argue for synergism. Don’t believe me? Here is Wesley’s quote from “Sermon 85: On Working Out Our Own Salvation”:
Even St. Augustine, who is generally supposed to favour the contrary doctrine, makes that just remark, Qui fecit nos sine nobis, non salvabit nos sine nobis: “He that made us without ourselves, will not save us without ourselves.” He will not save us unless we “save ourselves from this untoward generation;” unless we ourselves “fight the good fight of faith, and lay hold on eternal life; “unless we “agonize to enter in at the strait gate,” “deny ourselves, and take up our cross daily,” and labour by every possible means to “make our own calling and election sure.” (2.7)
In other words, St. Augustine, like John Wesley, is a synergist. On this part, the Catholic and the Arminian are at agreement on. The Catholic doctrine has never denied that man is involved in his own salvation and must make an effort to maintain it. So in certain aspects, the Arminian heresy maintains a similar soteriology to Catholic doctrine. However, both the Arminian and the Calvinist remain in the wrong.
In many senses, there are significant difficulties with interpreting St. Augustine, however, it must be considered that St. Augustine was attempting to resist as best as he could the Pelagian doctrines of no depravity whatsoever. I admit, I’m no expert on grace and free will but I can find nothing in St. Augustine’s actual writings that suggest he would have bought into Calvinistic and Arminian readings of his theology on original sin as relating to total depravity. He clearly argues that man has in him the desire to praise God (Confessions, 1.1) much as St. Thomas Aquinas argues that man retains a desire for the good. The theology of the Angelic Doctor permits no such thing as total depravity as the Arminians might admit to.
I answer that, The good of human nature is threefold. First, there are the principles of which nature is constituted, and the properties that flow from them, such as the powers of the soul, and so forth. Secondly, since man has from nature an inclination to virtue, as stated above (60, 1; 63, 1), this inclination to virtue is a good of nature. Thirdly, the gift of original justice, conferred on the whole of human nature in the person of the first man, may be called a good of nature.
Accordingly, the first-mentioned good of nature is neither destroyed nor diminished by sin. The third good of nature was entirely destroyed through the sin of our first parent. But the second good of nature, viz. the natural inclination to virtue, is diminished by sin. Because human acts produce an inclination to like acts, as stated above (Question 50, Article 1). Now from the very fact that thing becomes inclined to one of two contraries, its inclination to the other contrary must needs be diminished. Wherefore as sin is opposed to virtue, from the very fact that a man sins, there results a diminution of that good of nature, which is the inclination to virtue. (Summa Theologica, “First Part of the Second Part”, 85.1)
The problem is that for the Arminian, total depravity corrupts every single aspect of human nature. According to Arminian theologian, Dr. Roger Olson, “Arminianism teaches that all humans are born morally and spiritually depraved, and helpless to do anything good or worthy in God’s sight without a special infusion of God’s grace to overcome the effects of original sin” (Arminian Theology: Myths and Realities, 33). “Classical Arminianism agrees with Protestant orthodoxy in general that the unity of the human race in sin results in all being born ‘children of wrath'” (33). “Arminius, Wesley and classical Arminians in general affirmed inherited total depravity as utter helplessness apart from a supernatural awakening called prevenient grace” (27). According to Dr. Olson, because of the Arminian view on total depravity, it can be accurately said that because all are born into this state of total depravity, mankind has no free will apart from prevenient grace (75-76). This is exactly the Wesleyan view my Nazarene friends hold to.
Now, I should be careful to note that Arminians do insist that men are born retaining the image of God but this is not so. While Catholic doctrine agrees with Arminians and Calvinists in rejecting “that man may be justified before God by his own works…without the grace of God through Jesus Christ” (Council of Trent, Session 6, Canon 1) and therefore rejects Pelagianism as decreed in the Council of Orange, where Catholic doctrine rejects and finds fault in both Arminianism and Calvinism is that man is born totally depraved. True, man is born into a privation of sanctifying grace and his will is tainted by the fall as the Devil gains capacity over man  (CCC 407) but it is not totally tainted in that he still remains in his natural inclination toward God. According to Catholic doctrine, free will is an inherent part of being made in the image of God.
God created man a rational being, conferring on him the dignity of a person who can initiate and control his own actions. “God willed that man should be ‘left in the hand of his own counsel,’ so that he might of his own accord seek his Creator and freely attain his full and blessed perfection by cleaving to him.”
Man is rational and therefore like God; he is created with free will and is master over his acts. (CCC 1730) 
Catholic doctrine stands firmly against both Arminian and Calvinistic insistence on the view that we have utterly lost our free will due to the effects of total depravity. According to official Catholic doctrine, our free will is part of our inherent nature being created in the image of God. According to Calvinism and Arminianism, grace needs to act on us in order to restore our free will. And hence, despite the heretics’ insistence that they affirm men are created in the image of God, they deny this utterly. “If any one saith, that, since Adam’s sin, the free will of man is lost and extinguished; or, that it is a thing with only a name, yea a name without a reality, a figment, in fine, introduced into the Church by Satan; let him be anathema” (Council of Trent, Session 6, Canon 5) ultimately condemns both Arminian and Calvinist doctrines. Not either or.
There are additionally other bugs of Calvinism that Catholics would not agree with. For starters, limited atonement is rejected in favor of the “superabundant atonement” . In addition, Catholic doctrine would reject the idea of the notion that a true Christian cannot commit apostasy (CCC 2089). It might find room for loosely defined elements of unconditional election and irresistible grace as even Arminian theologians do but it is more probable to say that Catholic doctrine is more like -U-I- Calvinism if there are any traces of Calvinism in it at all. Arminianism seems to me to be more like TU-I- or TU-IP Calvinism. After all, Wesley was apparently a hair’s breadth away from Calvinism (Thorsen, Calvin vs. Wesley: Bringing Belief in Line With Practice, xi). Catholics remain a mile away from both.
1. The major distinction is that contrary to the Protestant view that men are snow-covered dung born into an entire mess, the Catholic view holds that men are dung-covered snow of whom someone else made a mess out of us.
2. See also, CCC 1701-1709 for further emphasis on this.
3. Summa Theologica, Third Part, Question 48, Articles 2 and 4.