Before William became king, how did England and France view one another? Were they diplomatic connections between the two kingdoms, such as royal marriages, or did both countries generally stay out of the other's business?
Best example I can think of off the top of my head are the three sisters from the Anglo Saxon kingdom of Wessex that married continental Kings in the 10th century. Eadgifu, Eadgyth, Eadhild were all married off to various Continental rulers as a way of building relationships with those powers.
Eadgifu was married to Charles III of France, and was the mother of Louis IV. There was a definite intention of drawing the two nations closer together - and less tension than there was after the 1066 Norman invasion. After that the two rulers became rivals for territory in Northern France and thugs changed dramatically.
Dunbabin, Jean (1999). "West Francia: The Kingdom". In Reuter, Timothy. The New Cambridge Medieval History.