French cuff
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A French cuff or double cuff (primarily British) is a cuff on a dress shirt that is folded back and then closed with cuff links or silk knots, instead of buttons. Cuff links and silk knots exist solely for shirts with French cuffs.
French cuffs are considered to be more formal than button cuffs. Although more formal, French cuffs are optional and a matter of preference. If a standard suit (as opposed to a dinner jacket) is formal enough for an occasion, then so are button cuffs. For a job interview in a business environment, shirts with button cuffs are generally preferred to those with French cuffs.
Alternatively, instead of cuff links, French cuffs can also be closed with the much less expensive, but just as formal and well-regarded, silk knots, sometimes called monkey's fists. Silk knots tend to be better known in Europe than in the United States.