No

Why? Because you should be inside at home! #StayHome

But if you absolutely had to go out to get groceries, medication or other essential travel, No, you don't need a jacket.

Based on the weather in Florence, Metropolitan City of Florence, Italy as of June 1, 2020 8:10pm local time.

Now

Clear
Temp: 76°F25°C
Wind: 5 MPH9 KPH
Precipitation: None

Today

Next 2 hours: No

Next 4 hours: No

Next 8 hours: Yes

Tomorrow

Yes

Clear throughout the day.
Low of 55°F13°C, High of 82°F28°C
Wind: 4 MPH7 KPH
Precipitation: 3% rain