This is sort of indirect answer, because I don't see why you would have non-free software on the system and not know about it. This is not to say you are wrong to want to check, but maybe first you want to stop and think if you really need to.
I'd like this functionality on Fedora
Fedora repositories are divided into 'free' and 'non-free'. By default, only the free repositories are used. So if you have never added any other repositories, then
yum cannot have installed anything from them.
It would of course have to include kernel modules, drivers and other binary blobs that are often allowed in distributions.
See this page. The only exception fedora makes is for "binary firmware", which is not required unless you are using certain hardware. I think you would know that too, but I can't promise.
I believe "firmware" technically is installed to a device, and technically it's already there anyway. Eg., your BIOS runs non-free software. On that level there is nothing you can do. You can also read fedora's discussion of "binary firmware" via the link on that page.
The kernel itself can't contain non-free code, it can only end up in a module. If you download the source from kernel.org and compile your own, I do not think it contains anything of that sort, since Linus's attitude ("I kind of accept them, but I never support them and I don't like them") implies non-free modules are allowed to be used with the kernel but very unlikely to be distributed by Linux proper (that is, kernel.org). The proprietary drivers are independently distributed; distros then include them, not kernel.org (however, according to that "Forbidden Items" page, fedora explicitly does not include proprietary drivers, at least in the default 'free' repos).
You could investigate online all the stuff listed by
lsmod. Since any binary blob has to be a module, methinks that's where you'll find it.
Fedora recommends that if you want to build your own kernel, you use a source package from them. However, I've used hand rolled kernels from vanilla kernel.org sources on fedora for years and never had a problem. So if you are comfortable doing that and don't use non-free repositories, you should not have any non-free stuff installed.