"forelsket", though it is slightly different. You are "forelsket" when you feel a strong emotional or sexual attraction to another person. Whereas "in love" can be at any stage of the relationship, it is put in the verb "forelsket" that it comes before loving someone. "for" = pre/prior/before, "elske" = love, so quite literally pre-love.
Though one would translate: "Jeg er forelsket i dig" into "I am in love with you".
That is not what in love means to us. It is not the first feeling, but the final feeling, the one that is not just an attraction but will last forever. People who say "I am in love with you." on a first date would probably use "forelsket", but they are not really in love. What do you say when you plan to spend the rest of your life with someone and the feeling is endless?
You misunderstand then. It is not on the first date, and remember this is just my personal experience with it and personal interpretation. At være forelsket is something you generally are during the "honeymoon" days, when everything is great and awesome and the other person is nothing but perfect. But when you plan to spend the rest of your life with a person then I guess you'd still say you "elsker" them? I'm not sure we make a distinction between loving as a family or as a girlfriend/boyfriend.