Different sources say different things. Wikipedia sums it up as follows:
The English possessive of French nouns ending in a silent s, x, or z is rendered differently by different authorities. Some prefer Descartes' and Dumas', while others insist on Descartes's and Dumas's. Certainly a sibilant is pronounced in these cases; the theoretical question is whether the existing final letter is sounded, or whether s needs to be added. Similar examples with x or z: Sauce Périgueux's main ingredient is truffle; His pince-nez's loss went unnoticed; “Verreaux('s) eagle, a large, predominantly black eagle, Aquila verreauxi,...” (OED, entry for “Verreaux”, with silent x; see Verreaux's eagle); in each of these some writers might omit the added s. The same principles and residual uncertainties apply with “naturalised” English words, like Illinois and Arkansas.
For possessive plurals of words ending in silent x, z or s, the few authorities that address the issue at all typically call for an added s, and require that the apostrophe precede the s: The Loucheux's homeland is in the Yukon; Compare the two Dumas's literary achievements. The possessive of a cited French title with a silent plural ending is uncertain: “Trois femmes's long and complicated publication history”, but “Les noces' singular effect was 'exotic primitive'...” (with nearby sibilants -ce- in noces and s- in singular).