This independence in England, plus the proximity of Normandy to other lands the French monarchy consider their own, makes France an immediate and obvious threat to deal with. England's new masters have a more modern approach to the art of warfare, and the will to utilise the country's rich resources to maximum effect.The English court may now speak French, but the Normans certainly don't consider their new conquest a French territory.
Most importantly, William the Conqueror came with the support of the Pope, as well as a mixed force of well-trained infantry, archers and heavy cavalry.
However, the new rulers of England have swiftly replaced and improved the taxation system so as to replenish their coffers in quick time. Having recently wrestled control of England from the Saxons, many would expect the conquering Normans to be somewhat spent and weakened.