French speakers: I need your input

You have helped me many times before with language questions. Here I am again. You’ve got a character sitting in a hotel in France writing a telegram to the U.S.  The year is 1884.

  1.  What would the telegraph office in the hotel be called (because hotels did have telegraph offices)?
  2.  How would the person write out the date and time? For example, an American at that time could write

 2 June 1884  8:00 a.m.

2nd June 1884 8 a.m.

June 2, 1884 8 am

but I’m pretty sure the time especially would be handled in a different way.

Any help much appreciated.