"How do I write the word fiance correctly?"

Fiancé is one of those words that were borrowed into English from French but haven't completely lost their French characteristics. In French, the ending is a masculine participial ending. This just means that when such a word is used to describe males, is the ending. When used to describe females, the ending is -ée. Therefore, when you talk of a man and woman who have become engaged, she is the fiancée and he is the fiancé. The pronunciation of both words, at least in American English, is the same: "fee-AHN-say" or "fee-ahn-SAY" (the latter is closer to the French pronunciation).