I'll answer you (the OP) as a native practitioner from hexagonal France, not as a linguist. I hear 2 things happening at once in your 1st example: 1. the v in veux kind of turned into a vowel, allowing the elision of the diphtongue eu; and 2. the syllable is not stressed like you would expect, as a non-native who trained your ear with careful speakers. I surmise this: the lack of stress, is what leaves you with the impression the whole vowel has disappeared, when native speakers confirm in comments it has not.
This is spoken French. The recommended elocution would be to pronounce all vowels, mark the liaisons and stress at predictable places, typically at the first consonant of the first non-grammatical word of each functional group:
Je veux z-attraper celui de minuit moins le quart.
Where a bold consonant indicates stress, like in poems in my 2nd grade reader: the syllable it starts is spoken louder, although not at a higher pitch like (I guess) you'd do in your native language. Even so, you've likely trained to rely on it for parsing spoken French, the same natural way as you use the tonal accent natively.
What I hear the 1st speaker utter instead is:
J' w' z-attraper ç'(l)ui de minuit moins l' quart.
Where ' is the elided e or eu, (l) the omitted liquid and w, the replacement of the voiced fricative v with a semi-vowel approximant: like midway between the English w and the German one. I surmise several things happened here:
- for stressing purposses, the utterer treats Je veu(x) as a grammatical word and the linked sibilant (transcribed as z-) as the first consonant of the verbal group;
- having elided the mute e in J(e) as is his wont he hits a snag: J'veux z-attraper is more difficult to pronounce than he anticipated, specifically more than Je v' z-attraper (where the elision of a diphtongue would be OK just before the stress);
- So he grabs both the butter and the coins that paid for it: he realizes the v as an approximant instead of a fricative.
This solves the problem of the double j-v consonant and allows to further elide the eu w/out meeting a problematic triple j-v-z: the approximant kind of doubles as a vowel, a very closed u.
Although it's off-topic, he hits an other elision snag later, in ç'lui: I hear him pronounce the syllable as in Switzerland, not as in sluice.
The 2nd example is more complex; the prescribed prosody would be:
je vais t'en faire voir de toutes les couleurs!
The rapper says s/th like:
ch'w' t'en fair' voir (d)'tout' les couleurs!
where ch transcribes the devoicing of the j and (d), the transformation of an unfeasible d'tout' into ttout'. Even native speakers get the impression of vais disappearing completely, because:
- it is not stressed,
- even the following syllable is not stressed,
- the elided vowel is an è, not the expected e.
Added after @jlliagre 's comment:
My post is emphatically not a phonetic analysis: it focuses on what I conjecture the speakers allowed themselves, especially which elisions, and the consequences they strived with; not on what we hear as a result. Accordingly, I tried to transcribe as maybe a novelist would represent spoken peculiarities in the direct speech: using the IPA in this role would miss the point and add to the confusion.