Looking at Wikipedia, besides the languages calling it cursive it seems there are two camps:
Germanic languages seem to call it "Writing letters/style" (German: Schreibschrift, Danish: Skråskrift, Dutch: Schrijfletter, Swedish: Skrivstil)
Romance languages seem to call it "cursive script" instead of just "cursive" (French: Écriture cursive, Italian: Scrittura corsiva, Portuguese: Letra cursiva)
Interestingly Italian calls italics "corsivo" and cursive "Scrittura corsiva" so the Wikipedia page for either has a disambiguation link to the other.