I was reminded in the Natural History Museum in New York that the Mediterranean sea was dry at some point.
If the connection to the Atlantic Occean was cut off, it would dry again. That is why it is so salty, especially in the East, it evaporates more than it can be replenished from rivers.
It did not take too long to go from there, to this video with graphics and some speculation about the consequences of no water in the Mediterranean.
How much of Europe would be a desert, how much deeper than the Grand Kanyon would it be, and how much higher the rest of sea level would be?