The answer you are likely looking for is the Atlantic Ocean, but in truth, there is no ocean that qualifies, since both countries are surrounded by bays, seas, gulfs, and straits. The closest ocean to France is the Atlantic Ocean and the closest ocean to Norway is the Arctic Ocean. However, the Atlantic Ocean is close to Norway as well.
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The Pacific Ocean borders both Russia's eastern border and the U.S.'s western coast. The Arctic Ocean borders both Russia's northern border and Alaska.