être mon amour means 'to be my love' in French.
Mon amour means 'my Love' in English.
I am excited to be with my love
I think you mean "tu es mon amour bébé" : you're my love baby
mon amour = my love
My lovely niece
je te manque mon amour? : do you miss me, my love?(tu me manques = I miss you)
"être" is the infinitive for "to be"; "mon amour" means "my Love". If the message was "be my Love / be my loved one / be mine", the French expression would be "sois (imperative mood for 'to be') mon amour / sois mienne". Hence the message certainly revolves about the same theme, even though it does not seems idiomatic in French.
Mon amour pour toi ne mourra pas means "my love for you will not die" in English.
Mon amour in French is "my love" in English.
all my love for ever
Je vais vous voir bientôt, mon amour. I'll see you soon, my love.
mon amour, mon chéri means my love, my darling boy