No, because ethnicity is typically defined in terms of people who share a common language, ancestry, history, society, culture, nation, or religion. Ancestry is in there, and it's true, almost everyone around the Mediterranean Sea has some common ancestry because there has been well over 2000 years of intensive commerce on that sea, but all the other typical markers of ethnicity are cultural, and Spanish, French, Italian, Greek, Turkish, Leventine, Egyptian and Berber (to name just a few) are certainly distinctly different ethnicities. They do share some things, but lumping them together is as silly as lumping Tlingits with Cherokees. Yes, they're both Native Americans, but their cultures are very different.