Catholics believe in Jesus Christ and His all-sufficient saving work on the cross (ours to receive by Grace Alone), just as Protestants do. We only deny an extreme Faith Alone position.
St. Paul opposes grace and/or faith to works in Scripture, only in a particular sense: the “works” of Jewish ritualism by which the Jews gained their unique identity (e.g., circumcision).
The Apostle Paul doesn't oppose grace, faith, and works, and in fact, constantly puts them together, in harmony. Here are two typical examples:
1 Corinthians 15:10 (RSV, as throughout) But by the grace of God I am what I am, and his grace toward me was not in vain. On the contrary, I worked harder than any of them, though it was not I, but the grace of God which is with me.
2 Corinthians 6:1 Working together with him, then, we entreat you not to accept the grace of God in vain.
Grace and works are for Paul, quite hand-in-hand, just as faith and works are. We Catholics only pit grace against works insofar as we deny (with Protestants) that man can save himself. Trent is very clear on that. We vigorously deny works-salvation. Scripture doesn't teach faith alone at all; nor do the Church fathers. In fact, the only time the phrase appears in the Bible, it is expressly denied:
James 2:24 You see that a man is justified by works and not by faith alone.
St. Paul states:
Romans 3:28 For we hold that a man is justified by faith apart from works of law. (cf. 3:20; 3:24: “justified by his grace as a gift”)
But “justified by faith” is different from “justified by faith alone”. The “works of the law” he refers to here are not all works, but things like circumcision. In other words, we are saved apart from Jewish rituals required under Mosaic Law. Paul makes clear that this is what he has in mind, in referencing circumcision in 3:1, asking rhetorically, “Are we Jews any better off? No, not at all” (3:9), multiple references to “the law” (3:19-21, 28, 31), and the following statement:
Romans 3:29-30 Or is God the God of Jews only? Is he not the God of Gentiles also? Yes, of Gentiles also,  since God is one; and he will justify the circumcised on the ground of their faith and the uncircumcised through their faith.
Paul is not against all “works” per se; he tied them directly to salvation, after all, in the previous chapter:
Romans 2:6-8 For he will render to every man according to his works:  to those who by patience in well-doing seek for glory and honor and immortality, he will give eternal life;  but for those who are factious and do not obey the truth, but obey wickedness, there will be wrath and fury.(cf. 2:13: “the doers of the law who will be justified”)
Paul uses the example of Abraham in Romans 4, in emphasizing faith, over against the Jewish works of circumcision as a supposed means of faith and justification (hence, he mentions circumcision in 4:9-12, and salvation to the Gentiles as well as Jews in 4:13-18).
Abraham's justification is also discussed in James 2, and there it is explicitly tied in with works, thus providing a perfect complementary (very “Catholic”) balance with Romans 4:
James 2:20-26 Do you want to be shown, you shallow man, that faith apart from works is barren?  Was not Abraham our father justified by works, when he offered his son Isaac upon the altar?  You see that faith was active along with his works, and faith was completed by works,  and the scripture was fulfilled which says, “Abraham believed God, and it was reckoned to him as righteousness”; and he was called the friend of God.  You see that a man is justified by works and not by faith alone.  And in the same way was not also Rahab the harlot justified by works when she received the messengers and sent them out another way?  For as the body apart from the spirit is dead, so faith apart from works is dead.
This is a wonderful cross-reference to Romans 4 in another respect: both cite the same Old Testament passage (Gen 15:6: seen in Rom 4:3 and James 2:23; also Gal 3:6). James, however, gives an explicit interpretation of the Old Testament passage, by stating, “and the scripture was fulfilled which says, . . .” (2:23). The previous three verses were all about justification, faith, and works, all tied in together, and this is what James says “fulfilled” Genesis 15:6. The next verse then condemns the notion of “faith alone” in the clearest way imaginable.
Scripture has to be interpreted as a harmonious whole. We Catholics can easily do that with these two passages. Roman 4 shows that the specific works of the Law that Jews lived by were not absolutely necessary for salvation, and that Abraham's faith was the key. James 2 is discussing the organic connection between faith and works in a general sense -- using the willingness to sacrifice Isaac as an example --, thus showing how “faith alone” is a meaningless and unscriptural concept. Faith can never be totally separated from works, except in initial justification, since (in Catholic teaching as well as Protestant) no work we do can bring us initially to justification: that is all God's grace.
James 2 is usually applied by Protestants to sanctification, but that’s not what the passage asserts. It mentions “justified” (dikaioo) three times (2:21, 24-25): the same Greek word used in Romans 4:2, as well as 2:13; 3:20, 24, 28; 5:1, 9; 8:30; 1 Corinthians 6:11; Galatians 2:16-17; 3:11, 24; 5:4; and Titus 3:7. If James actually meant sanctification, on the other hand, he could have used one of two Greek words ( hagiazo / hagiasmos) that appear (together) 38 times in the New Testament (the majority of times by Paul himself).