The demons believe and tremble but that is clearly not saving faith.
That would be intellectual assent but they clearly are not trusting Christ for their salvation. There is a receiving that is necessary.
John 1:10-13 He was in the world, and the world was made through him, yet the world did not know him. He came to his own, and his own people did not receive him. But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
Colossians 2:6-7 Therefore, as you received Christ Jesus the Lord, so walk in him, rooted and built up in him and established in the faith, just as you were taught, abounding in thanksgiving.
Then please understand that when Catholics say that faith alone is not enough they are speaking purely of intellectual assent, not what you are referring to as saving faith. Since, as I understand you, saving faith cannot exist without producing works, then I do not see how you differ on this point with Catholics other than in terminology.