Salvation is not by works. You need to study James a bit more.
So are you going to say if someone believes George Washington was the first president, that it means they have faith in George Washington? There is a huge difference between those two concepts. Many sinners believe Jesus died on the cross, but they do not have faith in that for their salvation.
I'll give you a perfect example, my father says he as "accepted Jesus as my savior" and that he believes "Jesus died on the cross for me"... however he also says that he is a "good soul" and a "good person", Me and my Dad got into a heated conversation when I explained to him that all his righteousness is as filthy rags in God's eyes, he said "so your telling me I have to humble myself before God and admit I am wicked and not good? No I am not doing that I am a good soul".
Does he really believe the Gospel the bible way is he really putting his hope in Jesus Christ? There are many people that use gospel terminology and give mental assent to certain aspects of the gospel of Jesus Christ, but very few who have put their hope and trust in Christ. Just like many believe George Washington was the first president of the U.S., but I know of no-one who is putting their trust and confidence in George Washington. So many do the same with the Gospel of Jesus Christ.
Consider what Vincent's Word Studies has to say about Hebrews 12:1:
"Faith (πίστις)
Without the article, indicating that it is treated in its abstract conception, and not merely as Christian faith. It is important that the preliminary definition should be clearly understood, since the following examples illustrate it. The key is furnished by
Heb 11:27,
as seeing him who isinvisible. Faith apprehends as a real fact what is not revealed to the senses.
It rests on that fact, acts upon it, and is upheld by it in the face of all that seems to contradict it. Faith is a real seeing. See Introduction, p. 363."
and see Gill on the passage:
" The "faith" here spoken of is not a mere moral virtue, which is a branch of the law; nor a bare assent to anything revealed, declared, and affirmed in the Gospel; nor a faith of doing miracles; nor an implicit one;
nor a mere profession of faith, which sometimes is but temporary; nor the word or doctrine of faith; but that which is made mention of in the preceding chapter, by which the just man lives, and which has the salvation of the soul annexed to it: and it does not so much design any particular branch, or act of faith, but as that in general respects the various promises, and blessings of grace; and it chiefly regards the faith of Old Testament saints, though that, as to its nature, object, and acts, is the same with the faith of New Testament ones; and
is a firm persuasion of the power, faithfulness, and love of God in Christ, and of interest therein, and in all special blessings: it is described as "the substance of things hoped for"; and which, in general, are things unseen, and as yet not enjoyed; future, and yet to come;"