"bit" (the english word) is pronounced exactly like "bite" (the french word), \bit\. The funny thing is that we often use "octet" to refer to bytes (which are pronounced /baɪt/ so no problems here) but we have no alternative for bit.
But in French, the word "bit" (as a French word) would be pronounced /bi/, as with dit ? That the French chose to continue to pronounce it in the English fashion suggests that they rather like the joke opportunity :-)
I don't know where you learned French or English for that matter but in my pretty mainstream accents English "bit" and French "bite" are not pronounced very similarly. I can't imagine a competent speaker confusing them.
I'm a native French, and the french wiktionary seems to agree with me https://fr.wiktionary.org/wiki/bitehttps://fr.wiktionary.org/wiki/bit : Both are pronounced \bit\. You can listen to the pronunciation and it's exactly the same. I remember a few jokes around this in university. I've also found this where a few people suggest pronouncing "bit" exactly like "bite".
I don't really know what else to say other that I'm French, went through university in France and we had this confusion.
Huh interesting. Must just be an accent thing. I have a southern US accent in English and American accent with SW France influences in French. To me they aren't that similar but I do see how they could be. You're the native speaker though so I don't really have a leg to stand on here.