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

Yes. Because of daylight saving time the gap moves between +8h and +9h.

When is the best time to call Vancouver from Paris?

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

Paris is 9h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.

Paris

France

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Vancouver

Canada

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

City	Time zone	UTC offset
Paris · France	Europe/Paris	UTC+2
Vancouver · Canada	America/Vancouver	UTC−7

What is the time difference between Paris and Vancouver?: Paris is 9h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +8h and +9h during the year.
Does the time difference between Paris and Vancouver change during the year?: Yes. Because of daylight saving time the gap moves between +8h and +9h.
When is the best time to call Vancouver from Paris?: There is no overlap between standard working days, so one side has to call early or late.