In later eras, and assuming separate nation states evolve in Britain and France, it seems to me that many wars would be fought for control of the isthmus and adjacent territory on either side, perhaps leading to the conquest of one side by the other before "WW1" and "WW2"
I think for the purposes of this thread we're assuming a large amount of convergence, so that events play out very much like OTL until 1940.