Had the same thing with France when I attacked Flanders (which I had released from Burgundy) as Utrecht. Apparently France will keep the provinces in the low lands because they want them, even if they don't have a claim. The AI will only hand over a besieged province if they don't want it themself, they don't even need to have a core or claim apparently. Problem is that if they have the capital you can't even vassalize them, because they will become a vassal of Milan instead of a vassal of you, which is even worse. Be carefull with the negotiations to look if they aren't becoming their vassal, because it made me ragequit my game as Utrecht like 15 min ago, because I gave them as a vassal to France by accident... I really hate this game sometimes.
Wait for them to peace out if making them your vassal isn't an option. Or perhaps just DoW Milan eventually, that might not even be that big of a problem. I gave my vassal to France by accident, so that made it impossible to take it in the next 100 years.. Perhaps with carefull planning, making alliances and waiting for the right time... Still I don't want to have to fight France over something that should have been mine...
Anyway... I know your pain, just curse at the game and hate it and then try to live with it or quit as I did... Start over and make sure to not make this mistake ever again XD