Is there any Saxon (native) word that contains /ʒ/? All words containing that sound I can think of such as genre, garage, luge, vision, visual, etc. are from French.
I would guess not, although I haven't made an extensive search. There don't seem to be many possible ways for it to develop according to the regular sound changes between Old English and Modern English.
I believe the main source of this sound is coalescence of early Modern English [zj] (as in vision), which often resulted from voicing of even earlier [sj]. This sequence occurred relatively often in loans from French or Latin, but I can't find any example from Old English.
Using the Phonetic Word Search, I did find a few words that can be pronounced with /ʒ/ that come from a native English root ending in s/z, followed by the Middle English suffix -ier. But this suffix seems to come from French, so the words as a whole are not native inherited vocabulary. These words are brazier (in the sense "brass-worker", from "brass" + "-ier"), glazier (from "glass" + "-ier"), and grazier (from "grass" + "-ier").
The sound /ʒ/ is commonly found in the sequence /ʒu/ or /ʒʊr/ (as in pleasure), which comes from /z/ followed by the French vowel /y/, which developed in English to /ju/. Some Old English diphthongs such as ew and iw also developed to /ju/ (as in sinew), so I suppose that could theoretically lead to a sequence /zju/ in native English that could coalesce to /ʒu/, but there don't seem to have been any Old English words with the right sounds in the right places.
The other source of this sound is recent loanwords from French with j/soft g. English generally doesn't have any consonants that developed to this sound (palatalized cg developed to the affricate /dʒ/).
Books about the history of English and the like generally describe its presence in English as due to French influence (often alongside the claim that French contributed to the phonological distinction between /s/ and /z/ and /f/ and /v/, which I find a bit more arguable: the process of intervocalic voicing of short /s/ and /f/ in English, followed by the shortening of long consonants and the loss of many word-final vowels, seems to have also played a pretty big role). E.g. see this passage from Trask's Historical Linguistics.