After having worked in the Moulin Rouge for some time, the female body wasn't a mystery to him -- but Christian's Victorian upbringing nevertheless demanded he give a woman her privacy in matters of undress. When Enigma quite literally stripped away the need for that privacy, he turned bright red and stammered something unintelligible in response.
The operator on the other line saved him from having to address her, and he turned away to have the quick conversation of what he'd heard and what their situation was. After having given Caritas' address and promising that he'd wait for the police to arrive, he disconnected the line and stood with his back to Enigma until she gave him the all-clear.
"Is there anything else you need?" he asked, while waiting. "Anything else I can do for you while we wait?"