Variant or diminutive form of baign; a small bathing place or bathing chamber.
From French baignet, diminutive of baigne/baign, indicating a smaller or more private bathing space than a public bathhouse.
The -et suffix in French (like in 'cabinet' and 'bonnet') turns big things into cute, small versions—so baignet is literally 'a cute little bath,' which tells you something about how the French view domestic comfort.
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