I cannot but wonder how you hear (read: perceive) cuisine being pronounced. When I listen to your two sources’ sound clips, I hear both using phonemic /ɪ/ for their unstressed vowel, sometimes shorter than other times.

In English, cuisine is phonemically /kwɪˈzin/, meaning that the first vowel is the KIT vowel but the second is the FLEECE vowel. In French, both are closer to the English FLEECE vowel, and there is no aspiration of the initial /k/.

So someone affecting a French accent in English might make them both the same, but otherwise you would not normally do so.

Because the first vowel is unstressed, it is subject to the customary reduction such vowels suffer in English, producing a wide possible range of phonetic realizations in which phonemic /ɪ/ becomes any of [ɪ̈], [ɨ̞], or [ə] phonetically.

If you cannot hear any difference between the unstressed vowels of roses and Rosa’s, then you or those you're listening to may have the weak vowel merger. You’ll also find wide variation in the unstressed vowel of naked along those same lines.

If you yourself cannot normally perceive sheep’s /i/ from ship’s /ɪ/, then you are like a great many who come to English with backgrounds in other languages which lack that particular phonemic distinction.