Left for France, showing little sensitivity (6)

I believe the answer is:

gauche

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'left' is the definition.
Both the answer and definition are adjectives. Maybe they are linked in a way I don't understand?

I cannot understand how the remainder of the clue works.

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(Other definitions for gauche that I've seen before include "left for Paris" , "not right for Parisian" , "inelegant" , "Graceless" , "Unsophisticated and socially awkward" .)

I've seen this clue in The Times.

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