Their legal page even refers to 'Red Hat’s Fedora Project' so as far as I'm concerned they're one and the same and can be dealt with as such. I'm not sure I am following your cleverness, it might be more productive to spell it out, and when making quotes in French you should at least try to do it right ;).
My post was not an IBM-owned-project but it evoked the idea of one inside the reader, much like Magritte