Both of them are correct, they just mean slightly different things.
I've found, which is the present perfect, means "as of this moment, I found someone (in the past)"; the present perfect is used to indicate that an action happened some time in the past but is related to the present.
I found, which is the simple past, just means "In the past, I found someone".
Ordinarily I would say that the present perfect would be a slightly more natural choice, but either of them works here. Here's a good page from the British Council on talking about the past and why you might choose one tense or another.
But it's not a good idea to look too deeply into song lyrics for grammatical correctness. Songs are often written to sound good rather than to be strictly correct.