It should be " I f I ever saw that you were falling, then I'd pick you up". However, in song lyrics you can get away with things that maybe aren't strictly grammatically correct, and "you're" (= "you are") is probably acceptable if it's necessary to fit the melody. Alternatively, you could say "If I ever see that you're falling, then I'll pick you up", which scans the same.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.