I saw it in the tale Le Vilain Caneton. I don't understand how come there's an inversion "es-tu" if it isn't a question?
The whole sentence:
Tu n'es pas comme les autres, peut-être es-tu une dinde !
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Regardless of whether it is explicitly a question or not, the inversion is the rule in French when a sentence starts with Peut-être unless it is Peut-être que.
Peut-être es-tu une dinde ! is very correct and literary.
Peut-être tu es une dinde ! is very incorrect but might be heard in lazy/broken/childish French.
Peut-être que tu es une dinde ! is what you commonly hear in spoken French.
This is not strange. You must pronounce it like an exclamation not a question.
it sounds better to me than "peut-être tu es une dinde !" (which is what most people would probably say nowadays).