I think that " Plat végétarien : Poulet " is just another part of this jokey menu: some other examples: "Assiette de palourdes « pas lourdes », Poutine à la Poutine, Non-profiteroles" etc.
Also, vegetarians in France (like me) are sometimes dismayed to find food described as 'vegetarian' actually containing chicken or bacon (lardons), so this is also something of a running joke.
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6 Feb. 2018