You have a point. Most of the major banks have closed down their offshore branches in recent years. You pick a bank, read their financial report, google their reputation, do the sign of the cross 3 times and take your chance.
If you find any bank offering high interest rates in euro currency then that is either a desperate bank or a bank in a country not so desirable...which makes it also a desperate bank and why they are︀ offering high interest rates...lol. Change your strategy from term deposits or just take the rates︁ the major banks are offering right now and ride it out. Don't take risks for︂ 0.5% or 1% difference in deposit rates.