I'm not sure I've ever heard someone pronounce 'bit' like 'bite' in French. But, in English, everyone pronounces 'coq' like 'cock'.
But the vowel is also different in cock [kɒk] vs coq [kɔk].
EDIT: I think I missed the point, if I'm reading "32 bits" in a french text then yes of course it sounds exactly like "32 bites".
My impression in France was that "bite" had the "i" sound slightly longer than in "bit". Some of the pronounciations at https://forvo.com/word/bite/#fr definitely lengthen it, but not all. Unfortunately there is only one recording for https://forvo.com/word/bit/#fr for comparison.
Then I remembered my telecom classes and we use octets because there's no confusion regarding byte sizes in older differet architectures.