This page has
5 links to information about bike paths in a few places. But, the US and Europe are big places. Is there are particular country in Europe or an area of the US you are interested in?
This page has
21 links to bike routes in the US. A few of them are off-road paths.
This link lists
bike paths in France.
I suspect that there are other pages in the archive (see my signature) and I'm sure that are other pages on the web that would be helpful to you.
Ray