"I am starting to like you, František."
Translation:Začínám tě mít ráda, Františku.
Sorry but nope. There are two separate issues.
"Začínám SE milovat" = I am starting to love myself.
Začínám TĚ milovat = i am starting to love you.
So SE TĚ is a mix that does not make sense.
The secon issue is love vs. like. Liking people not necessarily means loving them.