"Babe" is becoming very acceptable in youth speech. "baby" too as it is basic English.

Tout en prenant comte du rapport entre l'envoyeur et la destinaire du message on pourrait aussi entendre par exemple: ça va ma belle/biche/chère/etc ou même ça va mon amie.

Not only you need an idiomatic expression, but you need one tha can be butchered, if I may use that for a babe.
As you certainly know, opportunity for humor, puns and other speech "artifices" cannot alway be applied by a translator on the same part of the speech, but what is important is for it to be applied.
My first reaction was "Eh! Poupée ..." It had the right level of familiarity, but I could not see how you would integrate it into the rest. "Eh! cocotte ..." was a lot more adapted

Hope this helps you