This is an important question because it is the only thing in the letters of Paul that would place Jesus as having lived as a contemporary.
The traditional interpretation is that James and the other “brothers of the Lord” are the brothers from Jesus’ family, mentioned in Mark. But Paul and other early Christians also used familial terms (particularly brother) in a theological/metaphorical sense for their fellow believers.
(Insert argument & evidence for “brother of the Lord” as a designation, distinguishing James from being an apostle.)
So it’s hard to say exactly what Paul meant by “brother” without corroboration. And probably everyone reading this knows what corroboration we have: Josephus.
The problem with Josephus, though, is that scholars agree that the the versions we have of his work are tainted — specifically by later Christians with an agenda of proving the gospel version of Jesus’ life true.
some discussion of the two passages
Aside from Josephus, there are some other early writings about James.
Let’s be clear on which James we’re talking about. The James mentioned by Paul as “the brother of the Lord” is described by Paul as being part of the Peter, James, and John triumvirate leading the Jerusalem church. The writings of early Christian ??? describe “James the Just” as being the leader of the the early Christian church in Jerusalem (as does the Book of Acts), so I am going to assume that Paul’s James is this same person.
Mark’s triumvirate vs. Paul’s triumvirate
“James the Just” in other sources.
Epistle of James…?