It's because of the time zones, as I'm sure you had surmised.  Your 10AM
(EST) appointment is at 4PM Paris time (yes?) so it's natural that the folks
in Paris would see the appointment as it would occur in their local time.

It might be helpful if you each add the other's time zone to your calendar
page.  Right-click the list of times down the right side of the day view,
select "Change Time Zone" and then add the other time zone to the view.
That way you'll always be able to see the calendar in both Paris and NY
time.