because I doubt they even exist in tonal languages, although I am no expert

I suppose it depends on what you mean by accent. Many non-native speakers of Mandarin have what I would consider an accent. For example, a friend of mine from Canton has a noticeable Southern (Chinese) accent when he speaks Mandarin. He tends to replace x /ɕ/ and sh /ʂ/ with s /s/ and n /n/ with l /l/. He gets the tones right, though, Cantonese having 5 or 6 to Mandarin's 4.

Ceci n'est pas un seing.