Oui is usually read:
On occasion I hear oui read:
with an extra sound in the middle.
Is this common? Where and when will you come across such pronunciation?
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Approval is often expressed with ouais (pronounced /wɛ/, sometimes /we/) instead of oui (/wi/) in relaxed spoken French. The difference is similar to using yep vs yes.
A final /j/ might be heard in Switzerland as you noticed1.
This /wɛj/ variant is also present in Marseille, often with a prepended /v/ leading to voueï pronounced /vwɛj/.
1Note that there is no single French Swiss pronunciation. There are several different accents depending on the cantons (Geneva, Vaud, Valais, Jura, Fribourg...) and variations, sometimes also significant, inside them.
The normal pronunciation of oui is /wi/: a single syllable consisting of a semivowel followed by a vowel.
There is a very common variant which is spelled ouais and is pronounced /wɛ/. It's a colloquial word, which some speakers use a lot and others don't use much. Again, the semivowel /w/ is followed by a vowel /ɛ/: the word ends in a vowel sound. The vowel is nominally /ɛ/, an open-mid front unrounded vowel, which is the “è sound”.
In some accents (mostly from the south of France), /ɛ/ doesn't exist and /e/ (a close-mid unrounded vowel, the “é sound”) is used instead. Even in accents that do have separate /ɛ/ and /e/ sounds, some words always have /e/ (for example the “é” word ending), some words always have /ɛ/ (for example, in closed syllables, i.e. when there is a consonant after the vowel in the same syllable), and some words can fluctuate. A final /ɛ/ in a word is subject to fluctuation (as shown for example in regional variations for piquet and poulet) and many speakers have a degree of free variation between them. So pronouncing ouais as /we/ is fairly common, even though dictionaries only list /wɛ/ (and it even happens with speakers who would tell you that they only ever pronounce /wɛ/).
Adding a trailing /j/ semivowel is not a common variation. It isn't something I ever remember hearing. But it may be a regional variation that I'm not familiar with. (I'm French, and while've lived in Paris for most of my life and I meet people from all regions of France, I'm not particularly familiar with patterns of speech that people might drop when they move to the capital, and I don't know many Swiss French speakers.) The etymology of ouais is disputed, and it may have been influenced by other forms with a trailing /i/ or /j/ sound.
On the other hand, I'd be surprised by a two-syllable pronunciation /wei/, with the vowel /i/ at the end. It's really far from the mainstream pronunciation.
Are you sure of what you heard, though? I've noticed that to English native speakers, /ɛ/, /jɛ/ and /ɛj/ are barely distinguishable, whereas the same utterances sound completely different to a French speaker. English speakers commonly describe ouais as sounding like “way”, but to a French speaker it's more like “weh”: it's an open syllable.
There is a two-syllable pronunciation of oui, but it's /u:.i/, starting with a long /u/ and without an /ɛ/ or /e/ sound. It's uncommon and only used to mean “after some hesitation, I'm answering yes”, much in the same way that in English you can say “yyyyyes” starting with a long /i/.
« Ouais » (/we/) is a colloquial (familier) term used to say « oui » (TLFI). It can be used for a plain replacement nowadays. However, in the past this word was loaded with connotations and today it is still used that way (ironical, contemptuous, …).
In formal conversation you should avoid using this word; it is acceptable among friends or colleagues but considered by some people to be lax language if not vulgar.