It's because they're cognates that both come from Proto-Indo-European éǵ(ó)h₂.
Note that in French j comes from é and e comes from ó or h₂, while in Polish j emerged in Slavic languages and a comes from é. Their similarity nowadays is coincidental.
On the other hand, ty and tu both come from PIE túh₂ or tū́ and in this case similarity is not coincidental at all.
Proto-Indo-European is fascinating isn't it? So clever. I happened to be watching some cookery show the other day, and the term for a drier curry from somewhere on the subcontinent sounded like 'secca' - which obviously shares a route (via Sanskrit?) with the modern European languages.
Definitely no consonant at the end. 'y' is sometimes surprisingly difficult for non-natives to perceive (surprisingly, because to us it's just completely clear, but some people say that they don't hear a difference between 'e' and 'y'), you just have to get more listening experience.
It sounds more like the German 'ö' than 'ü'. German 'ü' sounds like a Polish 'i'.