Difficult to say...certainly our language would be different, as many norman french words made it into english....probably we would be a republic, as the absolute form of monarchy was not really a saxon thing. William enforced it post invasion. The influence of the Roman church would have been less, as the Franks were the strong arm of the church, the saxons tended to be slightly more secular.....
beyond that a lot can happen in a thousand years.
We'd also (probably) have a much more federal state, as the Saxon Kings of England were more "First among equals," whereas William centralised the country under his rule, eg. the Domesday Book, which was designed to see what he could tax.