Related: The Euro symbol always goes before the amount (like the dollar symbol) in English, no matter what country, as per the European Commission and leading publications. https://en.wikipedia.org/wiki/Euro_sign#Use
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In publications perhaps. I remember regularly seeing 3€50 in Greece I think and 3,50 € in Italy. Writing it differently and would look off or pretentious on a menu.
Placing the currency symbol after the amount is indeed the most common usage in Italy. I have no idea why, but if I had to guess, I think it might be because back when Italy had Liras the same pattern was used (i.e. 1000L instead of L1000).
I guess it's treated like physical units and pseudo-units: 0,5l of beer with 5% alcohol for 3,50€, that makes sense, no? ;)
(IIRC German typography says one should put a half-space between quantity and unit, and if that is unavailable, no space.)
3,50 € is the norm in Greece too. You say you regularly saw prices in the format <integral_euro>€<cents> in Greece? I've never seen that and I live in Greece; I surmise that either you don't remember correctly or that the set of the shops you visit is disjoint to the set of the shops I visit :)