The correct phrase is "a European." The article "a" is used before words that begin with a consonant sound, while "an" is used before words that begin with a vowel sound.
In the case of "European," the initial sound is /jʊərəˈpiːən/ which begins with a /j/ sound, which is a consonant sound. Therefore, you would say "a European."
"He is a European traveler."
Remember, it's the sound that matters, not the actual letter. So, even though "European" starts with the letter E, which is a vowel, it is the sound that determines the correct article to use.