A recent question here, Earliest recognition that Romance languages are related asks for when in history it was first noted that individual Romance languages were recognized as ... similar/related/coming from Latin/etc.
As has been answered there, it has always been obvious to anyone who knew two varieties. Between classical and vulgar latin, between medieval Latin and local patois, between the two most dissimilar, French and Romanian, there is just too much that is shared (even if for a full passage they are mutually unintelligible when spoken) not to be aware that something is the same.
But that is not the case for a comparison between Romance and Germanic. By years of scholarship, we know now that Romance and Germanic are two branches of Indo-European, including quite a few other far-flung (and not so far-flung) branches.
But the question here is when did that realization strike between Romance and Germanic? I expect that it was before Grimm made his sound-change laws in the early 1800's
Did the Roman scholars recognize any similarities of Latin with the varieties of language spoken by the Germanic tribes they encountered? Did medieval monks, from all over Europe notice anything between Old High German and Northern French? When did people realize the connection?