"I'm not a fool" is the simple phrase.
"Ain't" is still considered slang, even though the word has existed for a couple of centuries so far.
"No fool" is "not any fool" or "no kind of fool".
Don't worry about the double-negative here. Poor grammar has never stopped anyone from writing pop music. ;)
PS. I read it as "I ain't no fool". Using "it" doesn't make sense, you need to use "she/he", or even "there ain't no fool" (there is not any fool...)