I'd go with James' too.
Wiki states either are possible:
Singular nouns ending with an "s" or "z" sound
This subsection deals with singular nouns pronounced with a sibilant sound at the end: /s/ or /z/. The spelling of these ends with -s, -se, -z, -ze, -ce, -x, or -xe.
Many respected authorities recommend that practically all singular nouns, including those ending with a sibilant sound, have possessive forms with an extra s after the apostrophe so that the spelling reflects the underlying pronunciation. Examples include Oxford University Press, the Modern Language Association, the BBC and The Economist.[18] Such authorities demand possessive singulars like these: Senator Jones's umbrella; Tony Adams's friend. Rules that modify or extend the standard principle have included the following:
If the singular possessive is difficult or awkward to pronounce with an added sibilant, do not add an extra s; these exceptions are supported by The Guardian,[19] Yahoo! Style Guide,[20] The American Heritage Book of English Usage[21] Such sources permit possessive singulars like these: Socrates' later suggestion; or Achilles' heel if that is how the pronunciation is intended.
Classical, biblical, and similar names ending in a sibilant, especially if they are polysyllabic, do not take an added s in the possessive; among sources giving exceptions of this kind are The Times[22] and The Elements of Style, which make general stipulations, and Vanderbilt University,[23] which mentions only Moses and Jesus. As a particular case, Jesus' is very commonly written instead of Jesus's ? even by people who would otherwise add 's in, for example, James's or Chris's. Jesus' is referred to as "an accepted liturgical archaism" in Hart's Rules.
However, some contemporary writers still follow the older practice of omitting the extra s in all cases ending with a sibilant, but usually not when written -x or -xe.[24] Some contemporary authorities such as the Associated Press Stylebook[25] and The Chicago Manual of Style recommend or allow the practice of omitting the extra "s" in all words ending with an "s", but not in words ending with other sibilants ("z" and "x").[26] The 15th edition of The Chicago Manual of Style still recommended the traditional practice, which included providing for several exceptions to accommodate spoken usage such as the omission of the extra s after a polysyllabic word ending in a sibilant. The 16th edition of CMOS no longer recommends omitting the extra "s".[27]
Similar examples of notable names ending in an s that are often given a possessive apostrophe with no additional s include Dickens and Williams. There is often a policy of leaving off the additional s on any such name, but this can prove problematic when specific names are contradictory (for example, St James' Park in Newcastle [the football ground] and the area of St. James's Park in London). For more details on practice with geographic names, see the relevant section below.
Some writers like to reflect standard spoken practice in cases like these with sake: for convenience' sake, for goodness' sake, for appearance' sake, for compromise' sake, etc. This punctuation is preferred in major style guides. Others prefer to add 's: for convenience's sake.[28] Still others prefer to omit the apostrophe when there is an s sound before sake: for morality's sake, but for convenience sake.[29]
The Supreme Court of the United States is split on whether a possessive singular noun that ends with s should always have an additional s after the apostrophe, sometimes have an additional s after the apostrophe (for instance, based on whether the final sound of the original word is pronounced /s/ or /z/), or never have an additional s after the apostrophe. The informal majority view (5?4, based on past writings of the justices) has favoured the additional s, but a strong minority disagrees.[30]