"I am starting to like you, František."

[MESARCIK]

"Začínám se tě milovat, Františku." should surely be accepted.

[kacenka9]

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.

[MESARCIK]

Aah I see, thank you!