Does the time difference between Melbourne and Paris change during the year?

Yes. Because of daylight saving time the gap moves between +8h and +10h.

When is the best time to call Paris from Melbourne?

There is no overlap between standard working days, so one side has to call early or late.

Melbourne is 8h ahead of Paris. This gap is not fixed: daylight saving time moves it between +8h and +10h during the year.

Melbourne

Australia

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Paris

France

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A 9-to-5 working day in Melbourne does not overlap one in Paris at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Melbourne · Australia	Australia/Melbourne	UTC+10
Paris · France	Europe/Paris	UTC+2

What is the time difference between Melbourne and Paris?: Melbourne is 8h ahead of Paris. This gap is not fixed: daylight saving time moves it between +8h and +10h during the year.
Does the time difference between Melbourne and Paris change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +10h.
When is the best time to call Paris from Melbourne?: There is no overlap between standard working days, so one side has to call early or late.