1. What do you think of it?
It reminds me of "patricide" which is a bad thing. I like Patrick/Padraig but the female forms have never really appealed to me.
2. If you met a little Patricine? would you think it was a real name? Or would you think it was made up.
I would assume it was made up. It doesn't sound like a real name. I don't know if there is a French feminine form of
Patrick but if there is I'd guess it's
Patricie.