Surprisingly, it appears they are related, cognate to Frank.
The Wikipedia article that Alex B. linked gives an etymology for the Russian фря́зин /ˈfrʲa.zʲin/. It derives from the older form фрѧ́зин /ˈfrɛ̃.zʲin/ (following loss of nasality of ѧ and a spelling reform). This is a sound-changed version of /ˈfrɛ̃ɡʲin/ by progressive palatalization; this derives from Frank + /ʲin/, a suffix for ethnonyms.
The Thai ฝรั่ง [faràŋ] is reportedly also derived from Frank, via Arabic, Persian, or Sanskrit (various forms like Farangi, Faranj). Cognate terms were used by Middle Eastern traders to refer to the Catholic Western Europeans. Southeast Asian languages have numerous borrowings along that route, so this etymology is plausible. See also Wikipedia's list of cognate terms, which includes similar terms in many nearby languages (Indic languages, Malay, Cambodian). It also appears in Star Trek.
(Not related to English foreign, which is coincidentally similar.)