I have a 'conventional' bank account with a well known French 'rural' bank. My pension from the UK is paid into this and I use it to pay all the rates, insurance, water, 'phone etc;. Like most French banks it's charges are high, it's not very effecient and I need an (expensive) card to draw money out. I have now opened an online bank, Boursorama ( there are others ) I have a cheque book, card and all my banking is free. I use a transfer company to exchange my £ - euros from my British bank so pay little commision. It notifies me by sms when the account is used above a certain sum. This allows me to keep a strong control and stops fraudulent use.
I am very happy with it's services, I keep a minimum in my convential bank (for the moment) and have cancelled it's card therefore saving a large fee.