"Je t'aime" is much more a fixed idiomatic formula to express romantic love than it is in English. Particularly in American English you the phrase "I love you" is almost in inflationary use in many different situation. Not so in French.
That said, it is apparently OK to say "Je t'aime" to one's child, too. I have this on the authority of a Belgian mother. Though that might be different in some other French speaking parts of the world.
-- Chris (not a native speaker).