The style ruling you cite is not entirely consistent with regard to Massachusetts', New Orleans', and Paris's. That's not to say that it's wrong, but it does seem to be arbitrary—and it is by no means universally accepted by other publishing style guides.
For instance, here is a different guideline from Words Into Type, Third Edition (1974):
Proper names. The possessive form of almost all proper names is formed by adding apostrophe and s to a singular or apostrophe alone to a plural.
[Examples:] Jack's, Burns's, Dickens's, James's, Marx's, Adams's, the Davises', Schultz's, Schultzes'
Whenever the apostrophe and s would make the word difficult to pronounce, as when a sibilant occurs before the last syllable, the apostrophe may be used alone.
[Examples:] Moses' laws, Isis' temple, Xerxes' army, Jesus' followers
By convention, ancient classical names ending in s add only the apostrophe to form the possessive.
[Examples:] Mars' wrath, Achilles' heel, Hercules' labors
Because the last syllable of Massachusetts contains another sibilant besides the final s, the WIT guideline would render its possessive as Massachusetts'; WIT also agrees with the Merriam-Webster guideline on Paris's (assuming that we're talking about the French city and not the Trojan Helen-napper). But the WIT rule would seem to endorse using New Orleans's as the possessive of New Orleans.
The Chicago Manual of Style, Fifteenth Edition (2003) likewise has a lengthy, detailed, and ultimately arbitrary set of guidelines on this point:
7.18 Proper names, letters, and numbers. The general rule [to add an apostrophe and an s to indicate a possessive noun] covers most proper nouns, including names ending in s, x, or z, in both their singular and plural forms, as well as letters and numbers.
[Examples:] Kansas's legislature, Chicago's lakefront, Burns's poems, Marx's theories, Berlioz's works...
7.20 Names like "Euripides." The possessive is formed without an additional s for a name of two or more syllables that ends in an eez sound.
[Examples: Euripides' tragedies, the Ganges' source, Xerxes' armies
7.21 Words and names ending in unpronounced "s." To avoid an awkward appearance, an apostrophe without an s may be used for the possessive of singular words and names ending in an unpronounced s. Opt for this practice only if you are comfortable with it and are certain that the s is indeed unpronounced.
[Examples: Descartes' three dreams, the marquis' mother, ... Albert Camus' novels (the s is unpronounced) but Raoul Cumus's anthology (the s is pronounced)
In the Chicago system, the possessive forms of the three words that Merriam-Webster's uses as examples would be Massachusetts's, Paris's, and New Orleans's. I should note, however, that after delineating its system in great detail, Chicago blandly says "Those uncomfortable with the rules, exceptions, and options outlined above may prefer the system, formerly more common, of simply omitting the possessive s on all words ending in s." That would yield Massachusetts', Paris', and New Orleans'.
The Associated Press Stylebook and Libel Manual (2002) adopts the system that Chicago mentions at the end of its coverage:
SINGULAR PROPER NAMES ENDING IN S: Use only an apostrophe: Achilles' heel, Agnes' book, Ceres' rites, Descartes' theology, Dickens' novels, Euripides' dramas, Hercules' labors, Jesus' life, Jules' seat, Kansas' schools, Moses' laws, Socrates' life, Tennessee Williams' plays, Xerxes' armies.
For sheer consistency, you can't beat AP's guideline. Chicago and Words Into Type provide generally consistent guidelines and try to spell out rules for recognizing exceptions to the general rule. Merriam-Webster's Guide to Punctuation and Style doesn't identify the basis for exceptions to the general rule represented by "Paris's cafes"; it simply observes that "The possessive of ... some singular proper names ending in an s or z sound, is made by adding just an apostrophe." So should you write the possessive of Kansas as Kansas's or Kansas'? The MWGPS guidelines don't say, whereas the guidelines provided by WIT and Chicago do—though they lead to different conclusions.
I don't know how Merriam-Webster's Guide to Punctuation and Style came up with the advice it offers on Paris's, Massachusetts', and New Orleans', but the book doesn't seem to provide much predictive guidance for forming possessives of other proper names ending in s.
Update (January 7, 2022): Revised guidelines from CMoS
The information in my original answer (above) that refers to The Chicago Manual of Style's guidelines for handling possessives of singular proper names ending in s quotes from CMoS fifteenth edition (2003). However, CMoS sixteenth edition (2010) explicitly reverses those recommendations in two significant particulars, as follows:
7.17 Possessive of words and names ending in unpronounced "s." In a return to Chicago's earlier practice, words and names ending in an unpronounced s form the possessive in the usual way (with the addition of an apostrophe and an s). This practice not only recognizes that the additional s is often pronounced but adds to the appearance of consistency with the possessive forms of other types of proper names.
[Examples:] Descartes's three dreams, the marquis's mother, Francois's efforts to learn English, Vaucouleurs's assistance to Joan of Arc, Albert Camus's novels
7.18 Possessives of names like "Euripides." In a departure from earlier practice, Chicago no longer recommends the traditional exception for proper classical names of two or more syllables that end in an 'eez' sound. Such names form the possessive in the usual way (though when these forms are spoken, the additional 's' is generally not pronounced).
[Examples:] Euripides's tragedies, the Ganges's source, Xerxes's armies.
CMoS seventeenth edition (2017) retains the substances of these two changes. Although I composed my original answer in good faith (I didn't have a copy of CMoS sixteenth edition at the time), the guidelines that I cited were already obsolete at the time I wrote the answer.
