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

Yes. Because of daylight saving time the gap moves between −7h and −6h.

When is the best time to call Paris from Chicago?

Between 09:00 and 10:00 in Chicago, which is 16:00 to 17:00 in Paris.

Chicago is 7h behind Paris. This gap is not fixed: daylight saving time moves it between −7h and −6h during the year.

Chicago

United States

--:--:--

Paris

France

--:--:--

A 9-to-5 day in each city overlaps for 1h. That is 09:00–10:00 in Chicago, which is 16:00–17:00 in Paris.

City	Time zone	UTC offset
Chicago · United States	America/Chicago	UTC−5
Paris · France	Europe/Paris	UTC+2

What is the time difference between Chicago and Paris?: Chicago is 7h behind Paris. This gap is not fixed: daylight saving time moves it between −7h and −6h during the year.
Does the time difference between Chicago and Paris change during the year?: Yes. Because of daylight saving time the gap moves between −7h and −6h.
When is the best time to call Paris from Chicago?: Between 09:00 and 10:00 in Chicago, which is 16:00 to 17:00 in Paris.