Catholics do believe salvation by Grace alone.
Catholic USE THE WORDS "salvation by grace alone" but do not believe in salvation by grace alone as defined by scriptural context.
In scripture, grace denies any meritorious basis and always in contrast to works (Rom. 11:6). However, justification by faith is "by grace" (Rom. 4:16) and thus too in contrast to "works" (Rom. 4:3-6). In addition, justification by faith has reference to the substitutionary works and Person of Jesus Christ as its object (Rom. 3:24-26) which is also placed in contrast to our works.
Hence, the Biblical idea is that "justification is by grace alone through faith alone in Christ alone" in contrast to works.
What Rome does is separate and isolate grace from faith and faith from the works and Person of Christ in order to INCLUDE our works rather than to contrast it to works.
In fact the apostles James directly says it is not by faith alone. So your statment is false.
No, your understanding of James is false and you have jerked it out of context in order to pit it against the truth. In context James is directing it toward baptized believing church members by profession (James 2:1-9)whereas Paul is speaking about the justification of the "ungodly" (Rom. 4:5).
Again, Paul is dealing with justification by faith as a theological issue separate from regeneration whereas James is dealing with justification by faith in a professed regenerated person as a pragmatic issue. The distinction is clear if one has eyes to see. However, Paul agrees with James that a justified person is also a regenerate person and the fruit of regeneration is good works (Rom. 6-8; Eph. 2:10). Hence, pragmatically there is no such thing as an unregenerated justified person without good works.
However, the theological distinction set forth by Paul is that good works are the fruits of regeneration not justification as justification rests soley upon the good works of Jesus Christ, whereas the good works of regeneration are the manifest fruits of the indwelling Spirit of God.
You can deny this until your blue in the face but the contextual distinguishing factors between Romans 3-4 and James 2 will stand up against any rational line of attack you choose to take.