eM Client will display an event correctly adjusted for whatever time zone you are in. Say you have an event for 10am in Paris. As long as you setup the event correctly, and your OS is using your correct time zone, when you are in London, it will be correctly displayed in the calendar view as 9am. (See 1 below) If you are in New York, it will be correctly displayed as 4am. If you open the event, you will be able to see the original time and it’s time zone (See 2 below).
This works because eM Client gets your time and timezone from your OS. So the first step is to make sure that your OS settings are correct. If they are automatic, then they should change correctly as you travel across zones.