Which European country is the only one with coastlines on the Atlantic, the Mediterranean, and the North Sea? France. Metropolitan France reaches the North Sea in the north, the Atlantic Ocean along the west, and the Mediterranean Sea in the southeast.
This unusual combination comes from France's broad position across Western Europe. Its northern coastline includes the North Sea, while the English Channel separates much of northern France from Great Britain and connects the North Sea with the Atlantic. Along the west, France faces the Bay of Biscay and the wider Atlantic Ocean. The Mediterranean coast lies between Spain and Italy, including the French Riviera.
The wording refers to France's European mainland, often called Metropolitan France. France also has overseas territories, which give it additional coastlines and borders in the Americas, the Caribbean, the Indian Ocean, and the Pacific. Those overseas possessions are not needed to establish this answer.
Spain has both Atlantic and Mediterranean shores but no North Sea coastline. The United Kingdom borders the Atlantic and North Sea and has waters connected to the Mediterranean through Gibraltar, but it does not have a Mediterranean coastline in the usual geographic sense.