The great vowel shift happened after the Norman conquest, and there is no way that an infusion of French would create a language in which there is phonetic spelling.
Middle English (and Early Modern English) was spelled as it was spoken, to such an extent that there wasn’t consistent spelling, and people would just write whatever sequence of letters would get pronounced as the desired sound.
No, there is no such thing as "spelled as it was spoken" when everyone has inconsistent agreements on how to spell sounds and when a new language comes in with its own Latin spelling conventions that differ from the previous language.