Ty and wy, Tu and vous
Polish and French turn out to have similar words for you (singular) and you (plural). Did one language borrow from the other, or is this a shared indo-european root? I know that's a somewhat obscure question, but if someone knows, I'd be very grateful.
Yes, it's shared Indo-European root.
But unlike French “vous” (or Russian “вы” and other languages), “wy” is only used for second person plural in Polish and not for the polite form singular (In Polish, you uses the third person for that : “Czy pani chce coś ?” is literally “Does Madam want something ?” — in French you would say “Voulez-vous quelque chose ?”, the literal translation “Est-ce que Madame veut quelque chose ?” exists but is very formal).
Disclaimer : I hope I didn't make mistakes, my native language is French.
Actually, in some (rare) contexts wykanie (using the polite wy in Polish) happens. It was fairly common a few centuries ago, when common folk spoke to nobility, or nobility to monarchs and clergy. Later it has been used eg. in military, and one may encounter it eg. in Polish military movies. It is extremely rare though nowadays.
Wiktionary shows the etymology of these words. Short answer: yes, they share the same etymological origin. These words come from proto-Indo-European "tuh/tu". There's another word as well -- się which is the same as soi, coming from proto-Indo-European "swe" (self).
I'd guess "my" is another shared pronoun since Romance languages have nos/noi/nous which isn't too different from the accusative form nas.
I think it comes from further back than from French. I think it at least comes from Latin influence, but could go as far back as Indo-European.
Russian has "ты" and "вы" [в is pronounced like a v.]. Ukrainian has "ти" and "ви" [same].
Spanish has "tú" and "vosotros"(alternate feminine form"vosotras") and "usted" and "ustedes".
Portuguese has "tu" and "vocês".
Italian has "tu" and "voi".
Latin has "tu" and "vos".
German has something a bit different, yet similar "du" and "sie".
Dutch has "jij"(alternate form"je") and "U" and "jullie". (j sounds like an English y)
English has (old form "thou") and "you".
Swedish has "du" and "ni" for "you". (In Swedish, they do it the opposite and "we" is "vi" while in France "we" is "nous". Ever play telephone? Sounds change as you pass them along. In fact English "we" is closer to the Swedish "vi")
Marathi has "tumhī" spelled तुम्ही
Gujarati has "tame" spelled તમે but Hindi is different "aap" spelled आप
I am pretty sure it is a shared Indo-European root.
If you think about it, Italian tu and voi are similar as well.