Which "C41 processed B&W film"?
There are two kinds that I have run into.
There is the Ilford XP2 and the Portra B&W. There are others if I am not mistaken, but they tend to be like Portra.
Andwho.... The Ilford doesn't have a brown base. It has a clear base (well, not THAT clear...seems to be a bit denser than say Pan F). This means you MUST print it on regular B&W paper. Print it on color paper though and it all goes sepiaish. Nice film. I've used and gotten good results.
Now, the Portra stuff has the standard "color brown" base. It is designed to be printed on color paper. When printed on color it comes out B&W. Print in on regular B&W, and well, I guess it works like a color neg on B&W paper.