Hi Natalie,
i really don't know the correct pronunciation of your last name but if it simply sound like its written form Kusan, your name is a 100% Persian name but driven from the French word coussin. by this i mean its a word only used in Persia and Iran. and the meaning of Kusan+i (i-="descendant of", "attributed to" is that your ancestors somehow had a relation with kusan business or something like that.
like my name Sepasi means my ancestors had a strong relation with god. Sepas "Praying" or "thanks giving"