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From most to least frequent according to the Google Ngram Viewer: Rousseauian, Rousseauan, Rousseauvian, Rousseaunian.

The following forms are not frequent enough to show up on the Ngram Viewer, but I gather from Google search results that they do exist: Roussonian, Rousseavian, Roussevian.

If you went the etymological route, it would be "Russellian", but as far as I know nobody uses this as the adjective corresponding to "Rousseau".

Even though "Rousseauian" and "Rouseauan" are apparently the most common forms, I don't like the sound of the hiatus, so I think I personally prefer "Rousseauvian" (which seems to have become more common relative to "Rousseauan" in past decades).

I'd be interested in knowing if different forms are preferred in different languages. "Roussoniano" seems to have a fair amount of use in Spanish.

I kind of hate them all.

I'd be inclined to use Rousseauesque, even though the -esque ending typically expresses a different nuance.

I prefer Rousseauian

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ìtsanso, God In The Mountain, may our names inspire the deepest feelings of fear in urkos and all his ilk, for we have saved another man from his lies! I welcome back to the feast hall kal, who will never gamble again! May the eleven gods bless him!
kårroť

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@jsbaker750
seven-fifty.net

Rousski.

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Tibetan Dwarvish - My own ergative "dwarf-lang"

Quasi-Khuzdul - An expansion of J.R.R. Tolkien's Dwarvish language from The Lord of the Rings

Нет.

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ìtsanso, God In The Mountain, may our names inspire the deepest feelings of fear in urkos and all his ilk, for we have saved another man from his lies! I welcome back to the feast hall kal, who will never gamble again! May the eleven gods bless him!
kårroť

Rousseauois. All the vowels, all the time.

Leibnizian (much better than Rousseauist...)

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have a pic for the day...

-ian takes linking -v-

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Siöö jandeng raiglin zåbei tandiüłåd;
nää džunnfin kukuch vklaivei sivei tåd.
Chei. Chei. Chei. Chei. Chei. Chei. Chei.

Well, it can. My impression is that this usually occurs after a rounded vowel or with a w > v substitution (as in "Shavian" < "Shaw"); I don't think anyone would form something like "*Tennesseevian" from "Tennessee" or "*Paraguayvian" from "Paraguay". But words ending in /oʊ/ may correspond to -an adjectives ending in /oʊniən/; the basis seems to be Latin n-stems with nominatives in -o, like Cicero (adjective "Ciceronian"). Some examples that aren't built on Latin stems are the demonyms "Buffalonian" and "Torontonian". "Ohioan" has hiatus rather than -vian- or -nian.