If "this sentence is false" is true, then the sentence is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on ad infinitum.
Like I said, not a paradox, just nonsense.
Think of what "this sentence is false" means. It could mean "this sentence does not contain the necessary grammatical components to be called a sentence", which is obviously does according to the rules of grammar.
It's truth value isn't decided by any "if".
When you say "if this is true/false then..." then you are creating an axiom, divorcing the statement from it's meaning. So it's not a paradox, just an invalid axiom creating a paradox.
It works for any sentence. If I said "I am not a human being", it is clearly nonsense. I could however create an axiom, saying that "if that claim was true, it would be a paradox".