Is Jeanne a unisex name in France? 6.5 "How Are You?"

Module 6.5 How Are You? - The Formal Context:
Bonjour Madame. Permettez-moi de me présenter, je m'appelle JEANNE. (This can be spoken by a male or female if it were a unisex name, so far so good)

Then the person spoken to replied: 
Bonjour Monsieur. Je m'appelle JEANNE Rivière. Je vous ai parlé au téléphone hier.

Based on the reply the first person was NOT a female. In English there are quite a few unisex names: Leslie, Lynn, and Jamie, just to name a few. Is that a typo or unisex? 

I might be wrong, but I don't think that was actually a conversation between two people, or at least was not meant to be understood that way. I just think they (Rocket French) was just showing different ways to introduce oneself.  I really think "Jean" is masculine (sort of like John in English), and "Jeanne" is feminine.

Oh weird, my answer disappeared and so did M-L's response. But yes, it was three different types of formal self-introductions, all by Jeanne, the female speaker.

Bob-D,

Thank you for the belated response. torusan cleared that up for me a week or 2 ago. I don't know what the IT people are doing as he pointed out "weird".  Whatever they are doing I had one pleasant surprised when the points inside the green circle was credited exactly as it appeared. I usually get approximately 1/3 to half of the points credited. 

I'm really the only one with no imagination and flexibility in my brain, the only one who thought there were 2 people conversing, hence the silly question of "Is Jeanne a unisex name". In my heart I know it wasn't but I don't know all the English names in the world let alone French. It is better asked a silly question than making a mistake. 

Side bar: Personally I don't like unisex names especially if one is/was in the service industry meeting new people everyday and sometimes surprised when one was expecting a woman Lynn Smith but a man showed up.