This is something that's not 100% settled in English orthography, so it tends to be set down in usage guides. For example, here's what the Chicago Manual of Style (14th Ed) has to say:
"6.24 The general rule for the possessive of nouns covers most proper nouns, including most names ending in sibilants."
Examples they give include Kansas's, Ross's land, and Jones's reputation. Exceptions include Jesus' and Moses'.
By this, it would seem reasonable that possessive of the plural would be James', as with common nouns.
Note that this is not the entire story, but might (?) be the relevant bits.