What other big banks does Europe have that might stick around? Having all major banks US based would be a huge issue for Europe.
4 HSBC
7 BNP Paribas
10 Crédit Agricole
11 Deutsche Bank
12 Barclays
19 Societe Generale
20 Royal Bank of Scotland
Just as any company doing business in the US is bound by US law any bank doing business in the EU is subject to the laws of the member states.
And banking is a very well-behaved sector from an incentives (stick and carrots, regulation, microeconomics) perspective, so there will always be banks in the EU. (The question is the barrier to entry, and financial stability and consumer protection, not number of banks.)
But that's the direction of the world anyway. Most European regulators are actively trying to shrink their banks. This is certainly the case for UK and Swiss banks, less so for French banks.