The argument in favour of calling Middle English a pidgin comes from the extreme reduction in inflections from Old English to Middle English. The system of declension of nouns was radically simplified and analogized. The verb, also, suffered significant loss of older patterns of conjugation. Many strong verbs were remade into weak verbs. The subjunctive mood became much less distinct. Syntax, also, was simplified somewhat, with word order patterns becoming more rigid.
It has been argued that these grammatical simplifications resemble those observed in pidgins, creoles, and other contact languages, which arise when speakers of two different languages need to communicate with one another. These contact languages usually lack the inflections of either parent language, or drastically simplify them.
There are certainly grammatical changes, namely, the collapse of all cases into genitive and common. However, this process is due to the reduction of unstressed vowels to schwa due to afixed stress location. A fixed stress is the same in all of the Germanic Languages and thus has nothing to do with pidginization. And the reduction to schwas is well underway in all of the Germanic Languages. In addition, the process of case collapse was already underway in Old English. For example, in strong masculine nouns, the nominative and accusative cases were identical. So the loss of cases does not seem to support the conjecture that English is a creole.
There is other evidence. French and English both put auxiliaries before the main verb and invert them to make questions. In Old English, Verb-Subject-Object word order made questions. Today, and at that time, French used the same process to make questions. Today, English inverts auxiliary verbs and their subjects to make a question. If English was a pidgin, it seems logical to presume that VSO word order would continue to be used. The change, moreover, comes with Early Modern English, not Middle English; Shakespeare and the King James Bible continue to ask questions with the old pattern: Knowest thou?
No one denies that English had an unusual amount of French and Norman loanwords. However, most of the borrowing happened after 1400, two centuries after the nobility ceased to be French speaking. The most striking Norse borrowing, their pronouns, cannot be attributed to creolization either. It was a result of ambiguity between hiem and him etc. That was the cause of the borrowing. So vocabulary does not support the creolisation theory either.
Most Romance languages have only two grammatical genders. Masculine and Feminine. Most of Germanic ones have Masculine, Feminine and Neuter. These two gender systems are incompatible and so English responded by dropping genders altogether? Probably not. The loss of agreement between modifiers is attributable to the reduction to schwa.
The plural form in English originates from a neuter nominative plural and is cognate with the general Scandinavian plural ar. French's plural descends from oblique formations in Old French and is ultimately of pronominal, not nominal origin. So the plural forms have nothing to do with each other.
Most linguists hold that most changes that happened to English would have happened anyway, even without Norman influence. The Scandinavian languages have undergone very similar changes without the benefit of being conquered by the French.
There is at least one change that is a direct result of French infuence: the loss of Thou. Under Norman influence, Thou came to be parallel with Tu. Due to politeness among English speakers, Thou fell into disuse.
So English is probably not a creole. If it is, why are there 161 irregular verbs?