Ilford have made a few Fuji products over the years, inc the high speed B&W film and probably the B&W papers. However they have always been made to Fuji specifications and aren't just re-badged products.
This was why the Fuji B&W films weren't officially imported into the UK for many years, it was only because of companies importing from elsewhere that Fuji began selling them here themselves.
The Kodak 400CN is a fairly useless emulsion as it's designed for printing onto the long gone Kodak RA-4 process B&W papers via a colour head, or colour paper balanced to give a near B&W as possible. It's very poor for use with normal B&W papers.
It might surprise a few if I tell you I saw fresh Ilford Dia Positive film 35mm 36ex 100 EI last month in the Turkish Ilford importers shop, an E6 colour film which had made in Italy on the side of the box
Ian