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I think it's because French "U" is more like "Ю", only without [й] sound in the beginning.

Будьте = [бут'т'е] Prolonged soft "t"

Знаешь. Just ordinary Ш on the end. Ь is purely grammatical here.

Жить sounds like [жЫт']. Ж and Ш are always hard in modern Russian, that's why they teach...