"Related" being the operative word up there. And though "germane" is related to "germs" and "germination", and even to Jermaine Jackson in a distant sort of way, it isn't related to German. Probably.
Here's the deal. "Germane" comes from the Latin germanus, which means "full, own, as in one's own brother or sister". It is related to such words as genus and genre and gender through their common theorized ProtoIndoeuropean root, *gene--"to give birth or beget". At its base, then, germane means "having the same parents" (Or, apparently, grandparents. I discovered a term that has pretty much passed out of American usage, at least in my circles--the cousin-german, or first cousin. Not at all the same thing as a German cousin. Unless your cousin-german happens to actually be German.)
Now, as to the maybe so, maybe not connection to the word German, well, it gets a little tricky. And it shows up in that name Germain, because though this means brother, it can also mean, well, German. The Romans are the ones who gave us both. The first attested use of the written word "Germani" was by Julius Caesar, who was referring to a group of tribes in northeastern Gaul, but exactly who these people were is not certain. One theory has them as Celtic and the name Caesar used may have been given to them by the Gauls, and possibly meant "neighbor", which makes it not so ungermane after all. (Or it could mean "noisy" or "battle-cry", in which case, never mind.)
Interestingly, the word in its most current usage comes down to us from Hamlet, from Act 5, Scene 2, where Hamlet is preparing to duel Laertes. "The phrase would be more germane to the matter if we could carry a cannon by our sides." Apparently, this is the first figurative use of a now obsolete definition, meaning "closely related", to refer to things, not people.