When your friend talks about his pied-a-terre in the city, it's just his fancy way of mentioning the apartment he keeps there to stay in from time to time.
This borrowing from French, literally "foot on ground," designates a small second home. Dictionaries are in general content to stop their explanation of the origins of pied-a-terre by simply translating it, as if this were sufficient to explain how it inherited this meaning. On the other hand, it would hardly be a home if you didn't have your foot on the ground there some time.
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