Actually there was a successful (in a sense!) invasion of England by the French it was during the civil war called “The Barons War”. It was a war over King John’s refusal to acknowledge the Magna Carta. A future French King - Louis VIII backed the barons, landed with an army to support them and captured London and was crowned king there. He had a fair amount of support. In those days the difference between an Englishman & a Frenchman was mostly location. However he eventually got kicked out. The British don’t like to mention that this little slip up happened.
Also, Henry II, founder of the Angevin dynasty, landed an army and kept it in England as negotiations were under way for some kind of agreement over the succession — until the designated heir to the throne died, at which time the House of Normandy came to an appropriately ignominious end.