I listened to this doctor being interviewed on Sud Radio. He sounded so reasonable. He treats 40 women a day and has done so for 30 years. He is very sympathetic towards trans people. He explained how he simply isn't trained to deal with a transwoman. He apologised for using the vraie femme comment and has every sympathy.
He also explained how the situation went down. As far as I could gather the transwoman didn't even get past his secretary, and the situation got a bit heated there. The person then left a negative review on Google. He said he couldn't accept that his years of experience and reputation were being judged on a discussion with the secretary. Like judging an Airbnb by the wallpaper! He intends to defend himself in the courts. Sounds like a very kind, reasonable man - who will take no shit.
aside: I noticed he talked about "la personne"/"elle", which shows how the pronoun question doesn't come up in French. You can call anyone a "personne", male or female, and still continue the sentence using elle.