The kind you're talking about is the type used by delicatessen - either light chocolate brown, golden brown or usually white, seasonned with seeds? (it is really good. I agree with you - my city is even famous for it)

It's called "rye bread' on our side of the ocean, but it's made mostly with wheat flour with a small percentage of rye flour, mostly for flavour. There's a bit more in the chocolate brown type, but really not much if you're talking about the white type.

Real "rye bread" is the very dense black bread type. People of French descent/culture hate it so much that we still have this expression "(you) have to eat (your) black bread" which means an euphemism to say someone is copping with extreme poverty/misery.