What is the ruling on borrowing from European banks to purchase a home, given the existence of an Islamic bank that operates on a percentage basis until the amount is repaid?

It is impermissible to borrow from an interest-based bank, with interest, to purchase a house or anything else, except in a case of dire necessity. As for purchasing through an Islamic bank using the method of Murabaha (cost-plus financing) that is Sharia-compliant, there is no objection to it, provided its conditions are met, and that the profit margin is known. The important thing is that a genuine Murabaha transaction takes place, not a trick to circumvent riba (usury/interest).