A question on Yahoo! Answers, "What would English look like today without the French influence?", prompted me to a rethink. Interesting though these attempts are, they're essentially modern English, removing French and Latin but retaining all the innovations (such as the massive simplifying of grammar) that marked the vast 'reboot' from Old English (aka Anglo-Saxon) to Middle English and later Modern English.
An English (let's call it 'Anglick') where no Norman invasion happened would more likely be an entirely different branch of the Germanic languages, even more dissimilar to English than Yola, with many more features akin to Old English (for instance, it might - like modern German - retain grammatical gender and case endings). I imagine the Lord's Prayer in Anglick could look like this ...
Vaider arn thu beest on evvinem... and even this, as the language of the King James Bible is to English, could be archaic Anglick. Who knows where English could have borrowed from?
Gehagled be thi narmer
Becoom theen kernyrike
Gedaan theen villa
On arder soso on evvinem
Arne daglicke brode geev uns hoady
An ar gildies uns vergeev
Soso weer andern gildeen vergeeven
An nae layde thu uns in costening
Arba layde thu uns vorm ooble. Zo beest.