Opening a bank account will go a whole lot smoother once you're actually living in France. Usually they want you to make an appointment (often the same day) and come in with your last three months' of pay slips (basically proof of income - your pension will do), proof of residence (normally an electric bill) and the usual round of identification (passports or whatever).
The immobilier should be able to help you figure out how to make the necessary deposits.
Which order to do things (rent in France, let in England) is pretty much up to you. The risks are fairly evident. You have to figure out what you could work around if one side of the transaction should fall through (and with the current economic situation, it's probably best to assume something will go wrong. If it doesn't, it will just be a happy surprise.)