Pouch

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Middle English (as a noun): from Old Northern French pouche, variant of Old French poche ‘bag’. Compare with poke2.

wiktionary

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From Middle English pouche, poche, borrowed from Old Northern French pouche, from Old French poche, puche (whence French poche; compare also the Anglo-Norman variant poke), of Germanic origin: from Frankish *poka(“pouch”) (compare Middle Dutch poke, Old English pohha, dialectal German Pfoch). Compare pocket, poke.

etymonline

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pouch (n.)

early 14c. (late 12c. as a surname), pouche, "bag worn on one's person for carrying things," especially (late 14c.) "small bag in which money is carried," from Anglo-French puche, Old North French pouche (13c.), Old French poche "purse, poke," all from a Germanic source (compare Old English pocca "bag;" see poke (n.1)). Extended to sac-like cavities in animal bodies from c. 1400.

pouch (v.)

1560s, "put in a pouch;" 1670s, "to form a pouch, swell or protrude," from pouch (n.). Related: Pouched; pouching.