[Sorry for the serious wall of text.]

I've heard those claims, too. They're incorrect.

A creole is born from a pidgin (language fragments) glued into a coherent whole by grammatical rules made "on the spot". Because of that, it's practically impossible to analyse the grammar of a creole as the result of mutations over the grammar of any parent language.

However you can do it with English just fine:

• Phonetic erosion makes the case suffixes identical → case is now marked by word order → word order becomes syntactically fixed. Now you can't say *"your famous blue raincoat at the shoulder torn was" without sounding like a weirdo.
• Phonetic erosion screws with the grammatical gender → grammatical gender gets ditched
• Phonetic erosion merges a bunch of verbal conjugations together → pronouns become obligatory + you need to spam aux verbs to convey subtler distinctions.

Even weirder features like do-support are easy to explain if you look at other Germanic languages (e.g. some German dialects spam tun "do" in a similar way.)

As a counterexample, look at Haitian - an actual creole, with the main parent languages being Fon and French. If you try to explain it as a grammatical descendant of either, you hit a wall already in the plurals:

• Fon: a-nòmàá "bird" vs. ǹ-nòmàá "birds" (source)
• French: l'oiseau /lwa.zo/ "the bird" vs. les oiseaux /le.zwa.zo/ "the birds"
• Haitian: zwazo "bird" vs. zwazo yo "birds"

Fon marks the plural mostly in the noun itself. French in theory does it, but most of the job is done by closely connected determiners, articles, and pronouns. If Haitian simply inherited the plural from either, you'd expect it to be marked before the noun, as a prefix of sorts. It doesn't: the plural marker is a free word that goes after the noun phrase. And it is not bound to the noun, as zwazo mwen yo "my birds" shows.

I don't think that contemporary English can be even remotely explained by creolisation. The Romance lexical influence is easier to explain if you had some sort of bilingual ruling chaste, exerting pressure over the language over a few centuries. One that would eat bœuf and porc while the plebs were raising cows and pigs. ...and, well, that's exactly what happened.