Julie was my first love, I’m so happy to see it used!
From your list, I love [name_f]Claire[/name_f]. It’s sophisticated and timeless, with the classic and sweet [name_u]Julie[/name_u]. I think they are perfect together. [name_f]My[/name_f] second choice would be [name_f]Natalie[/name_f] as it gives me the same feeling as [name_u]Julie[/name_u] does, but the two -ie endings is giving me pause. If that doesn’t matter to you, that’s another great option.
I think all your names pair nicely with [name_u]Julie[/name_u]. [name_f]My[/name_f] favourite is [name_f]Claire[/name_f], but you really can’t go wrong.