I thought French already had a Germanic-based grammatical structure.
Not really. Not at all, actually.
There's a difference between grammar and lexicon. While French and English, or French and German, may share lots of vocabulary, that doesn't mean that grammar, the structure of the language, shares the same relationship. For instance, while Modern English is made up of a significant amount of Romance-based lexicon, its grammar is inherently Germanic. One instance of this is English's tendency towards satellite framing. That is, English uses particles/adverbs to describe manner and direction in verbs (consider the difference between
go in and
go out versus
enter and
exit; the distinction in the former is not a part of Romance-language grammar and instead different verbs are used).
Grammar is the primary consideration when dividing language families up and proposing links between languages, something which is quite confusing when the languages share a significant portion of their lexicon. The prime examples here are the Altaic proposal (comprised of Turkic, Mongolic, and Tungusic branches), which are likely just different families with similar lexicon due to continuous contact (which makes the rare inclusions of Japonic and Koreanic even odder). Also is the relationship between Chinese and Vietnamese. Sino-Vietnamese vocabulary makes up an enormous proportion of the Vietnamese language, though grammatically, Vietnamese is closer to (e.g.) Khmer than Chinese, by an enormous margin. But I digress, I suppose.
Indeed, English is not at all "German with a French grammar"--in fact, it's more of "French with a German grammar" (more is relative: in this case, the comparison is still quite far from the truth), and in this sense I agree with Alon. The point being, as Germanic languages, English and German are much closer on a kinship basis. The same would hold true between French and German.