Hijabs are banned from French schools, not all French public places. It's the burqa and niqab that have been banned everywhere.Not true.
I`d imagine it`s just as illegal for a Christian to wear the Hijab in Paris as it is a Muslim.
However, I'm sure you're right: it would be unacceptable for any Christian in Paris to wear a hijab. Christians have never been associated with anything like the hijab... certainly not, say, the city's patron saint. And I'm sure that any Parisian would automatically dismiss someone dressed like this as entirely un-Christian: