Your answer has "Catholicism" tag, so I'll try to explain Catholic belief that Paul and James are in perfect harmony, that they say the same, just from two perspectives.
Let's start with James. He wrote in the second chapter of his letter:
14 What good is it, my brothers and sisters, if someone claims to have
faith but has no deeds? Can such faith save them? 15 Suppose a brother
or a sister is without clothes and daily food. 16 If one of you says
to them, “Go in peace; keep warm and well fed,” but does nothing about
their physical needs, what good is it? 17 In the same way, faith by
itself, if it is not accompanied by action, is dead.
18 But someone will say, “You have faith; I have deeds.”
Show me your faith without deeds, and I will show you my faith by my
deeds. 19 You believe that there is one God. Good! Even the demons
believe that—and shudder.
20 You foolish person, do you want evidence that faith without deeds
is useless? 21 Was not our father Abraham considered righteous for
what he did when he offered his son Isaac on the altar? 22 You see
that his faith and his actions were working together, and his faith
was made complete by what he did. 23 And the scripture was fulfilled
that says, “Abraham believed God, and it was credited to him as
righteousness,” and he was called God’s friend. 24 You see that a
person is considered righteous by what they do and not by faith alone.
The kind of deeds James is writing about are helping the needy and other actions that true faith (accompanied with true love) makes absolutely natural. No sacrifice in temple, but serving Christ in the poor, not because law orders to do so, but because you believe and recognize it as God's will.
Abraham is a good example: he has no law to obey, but obeyed God because he believed in him. The sacrifice of Isaac wasn't a work to deserve justification regardless of faith, it was an act of obedience to God's will, or faith in action.
James don't criticize faith, but he criticizes faith that remains theoretical, with no action induced by it, with no fruits of the Spirit. If you don't reflect your faith in your life, it remains just a theory.
Have you ever been to Antarctica? I assume not. Even though you have only testimony of others (through pictures, interviews with travellers, labels saying that penguins in a zoo are from there etc.), you believe the continent exists. But does this belief make you a better person? If you are not an exception who wants to go there and helps others go there too, there's no good fruit of this belief. we don't know what demons know for sure, but there are other things they just believe in, and they believe in them like we believe in Antarctica. And if we believe in God this way, we are neither cold nor hot (see Revelation 2:15), and we can't expect this faith to justify us.
On the other hand, Paul never proposes faith without the kind of deeds James requires. Paul criticizes deeds without true faith, deeds that should merit salvation by themselves. But there are many passages in his letters, where he requires the kind of deeds James writes about. Just as the first example I found in brief search, I picked Ephesians 5:3-9:
3 But among you there must not be even a hint of sexual immorality, or
of any kind of impurity, or of greed, because these are improper for
God’s holy people. 4 Nor should there be obscenity, foolish talk or
coarse joking, which are out of place, but rather thanksgiving. 5 For
of this you can be sure: No immoral, impure or greedy person—such a
person is an idolater—has any inheritance in the kingdom of Christ and
of God. 6 Let no one deceive you with empty words, for because of
such things God’s wrath comes on those who are disobedient. 7
Therefore do not be partners with them.
8 For you were once darkness, but now you are light in the Lord. Live
as children of light 9 (for the fruit of the light consists in all
goodness, righteousness and truth)
"No immoral, impure or greedy person has any inheritance in the kingdom of Christ and of God" - what else should it mean than that it's necessary to live as children of light to be saved? How should faith that won't bear fruits of goodness, rightousness and truth lead to justification? And how one should be good, righteous and truthful if it is not reflected in their everyday life, in their everyday deeds? This is essentially what James wrote.
James focuses on "faith without deeds is dead" and Paul on "deeds without faith are in vain", but both say the same: both is necessary. Both agree that to accept God's grace by faith is first and more important, but this necessarily leads to good deeds, so lack of deeds indicate lack of faith.
This is essentially what Catholic Church teaches. Here is an example of a good article discussing Catholic view on justification in detail.