I've worked for two credit card processing companies, and I happen to know that French credit card payment processing is not remotely like that of any other country. I am not surprised by your experience. The big four banks process for everybody else, in their own format...
The French, on the whole, do not like credit cards per se, and most banks only offer an extended debit card, where you pay off the balance at the end of the month or there's the devil to pay. My Credit Agricole "Visa" card is a straight debit card, apart from the bank's blithe disobedience of Mastercard and Visa regulations, like being able to change your pin at an ATM. But then CA is a consortium of small local banks that don't quite talk to each other, not in the same language, anyway. Any change must be wrought by that many-legged idiot, a committee. And how many of us have experienced the deep joy of finding their (British, Canadian) Visa or Mastercard won't pay for petrol in a 24/24 service station and there's about a teaspoonful left in the tank?
It really depends on the nature of your business and the types of sale you are planning. Unless you're a corporate entity swinging a lot of weight, and expecting a lot of transactions, or are backed by one (I'm thinking Amazon here) approaching a French French bank for reliable e-services just isn't worth it. There are the International French banks - HSBC, for instance - who process for themselves. Good hunting.
PS I don't work for HSBC or any of their associates! There are other banks! And Worldpay and -er- Paypal.